ELECTROSTATICS

Total number of Questions in this chapter are :

(i) Level # 1 ....................... 118

(ii) Level # 2 ....................... 39

(iii) Level # 3 ....................... 40

(iv) Level # 4 ....................... 52

Total no. of questions ....................... 249

 LEVEL # 1
Questions
Q.7 If a glass rod is rubbed with silk, it acquires
based on Charge & its properties a positive charge because -
Q.1 The ratio of electric force (Fe) to gravitational (A) Protons are added to it.
force acting between two electrons will be: (B) Protons are removed from it.
(A) 1 × 1036 (B) 2 × 1039 (C) Electrons are added to it.
(C) 6 × 10 45 (D) 4 × 1042 (D) Electrons are removed from it.

Q.2 Fg and F e represent the gravitational and Q.8 Which one of the following is the unit of
electrostatic force respectively between two electric charge ?
electrons situated at some distance. The (A) Coulomb (B) Newton
ratio of Fg to Fe is of the order of - (C) Volt (D) Coulomb/Volt
(A) 1036 (B) 101
(C) 10º (D) 10–43 Q.9 An accelerated or deaccelerated charge
produces-
Q.3 One quantum of charge should be at least (A) Electric field only
be equal to the charge in coloumb: (B) Magnetic field only
(A) 1.6 × 10–17 c. (B) 1.6 × 10–19 c.
–10
(C) Localised electric and magnetic fields
(C) 1.6 × 10 c. (D). 4.8 × 10–10 c.
(D) Electric and magnetic fields that are radi-
ated
Q.4 The unit of charge is coulomb in SI system
and esu of charge (or stat coul) in C.G.S.
Q.10 W hich one of the f ollowing statement
system 1 coloumb equals
regarding electrostatics is wrong ?
(A) 3 × 109 esu (B) (1/3 × 109)esu
8 (A) Charge is quantized
(C) (1/3 × 10 ) esu (D) (9 × 109) esu
(B) Charge is conserved
(C) There is an electric field near an isolated
Q.5 The relative strengths of grav itational, charge at rest
electromagnetic and strong nuclear forces are-
(D) A stationary charge produces both electric
(A) 1 : 1039 : 1036 (B) 1 : 1036 : 1039
and magnetic fields
(C) 1 : 10-26 : 10-39 (D) 1 : 10-39 : 10-36

Q.6 An electron at rest has a charge of 1.6 × 10–19 C. Q.11 The dielectric constant for water is -
It starts moving with a velocity v = c/2, where (A) 1 (B) 40
c is the speed of light, then the new charge (C) 81 (D) 0.3
on it is -
(A) 1.6 × 10–19 Coulomb 1
Q.12 In M.K.S. System, 4  equals -
2 0
 1
(B) 1.6 × 10–19 1   Coulomb (A) 9 × 109 N-m2/C2
2
(B) 1 N-m 2/C2
2 (C) 1 dyne - cm 2 / stat C2
2
(C) 1.6 × 10–19    1 Coulomb (D) 9 × 109 dyne x cm2 / stat C2
1

1.6  10 19 Q.13 A stationary electric charge produces-

(D) Coulomb (A) Only electric fields
2
 1 (B) Only magnetic field
1  
2 (C) Both electric as magnetic field
(D) Neither electric Nor magnetic field
Q.14 Charges reside on the - Q.19 The force between an  -particle and an
(A) Outer surface of the charged conductor electron separated by a distance of 1 Å is -
(B) Inner surface of the charged conductor (A) 2.3 × 10–8 N attractive
(C) Inner as well as outer surface of the (B) 2.3 × 10–8 N Repulsive
charged conductor (C) 4.6 × 10–8 N attractive
(D) 4.6 × 10–8 repulsive
(D) None of the above

Q.20 Two charges are at distance (d) apart in air.

Q.15 An isolated solid metallic sphere is chargrd Coulomb force between them is F. If a
with +Q charge .The distribution of their +Q dielectric material of dielectric constant (K) is
charge on the sphere will be placed between them, the coulomb force now
(A) uniform but on the surface alone becomes.
(B) non uniform but on the surface alone (A) F/K (B) FK
(C) uniform inside the volume (C) F/K2 (D) K2F
(D) non uniform inside the volume
Q.21 Two point charges in air at a distance of 20
cm. from each other interact with a certain
Questions force. At what distance from each other
based on Coulomb's Law
should these charges be placed in oil of
relative permittivity 5 to obtain the same force
Q.16 Two similar charge of +Q , as shown in figure of interaction –
are placed at A and B. –q charge is placed (A) 8.94 × 10–2 m (B) 0.894 × 10–2 m
at point C midway between A and B. –q (C) 89.4 × 10 m–2 (D) 8.94 × 102 m
charge will oscillate if
 Q.22 A certain charge Q is divided at first into two
parts, (q) and (Q-q). Later on the charges are
+Q C +Q placed at a certain distance. If the force of
 –q
 interaction between the two charges is
A B maximum then-
 (A) (Q/q) = (4/1) (B) (Q/q) = (2/1)
(C)(Q/q) = (3/1) (D) (Q/q) = (5/1)
(A) It is moved towards A.
(B) It is moved towards B.
Q.23 A unit charge is one which when placed in
(C) It is moved upwards AB. vacuum one cm from an equal charge of the
(D) Distance between A and B is reduced. same kind will repel it with a force of-
(A) 1 Newton (B) 1 dyne
(C) 2 dyne (D) 4 dyne
Q.17 When the distance between two charged
particle is halved, the force between them
becomes - Q.24 The permittivity o of vacuum is 8.86 x 10-12
(A) One fourth (B) One half C2/N-m2 and the dielectric constant of water
(C) Double (D) Four times is 81. The permittivity of water in C2/N-m2 is-
(A) 81 × 8.86 × 10–12 (B) 8.86 × 10–12
Q.18 The force between two point charges in (C) (8.86 × 10–12)/ 81 (D) 81/(8.86 × 10–12)
vacuum is 15N, if a brass plate is introduced
between the two charges, then force between Q.25 The force between two point charges placed
them will- in vacuum at distance 1 mm is 18 N. If a
(A) Becomes zero glass plate of thickness 1 mm and dielectric
constant 6, be kept between the charges then
(B) Remains the same
new force between them would be-
(C) Becomes 30 N (A) 18 N (B) 108 N
(D) Becomes 60 N (C) 3 N (D) 3 × 10–6 N
Q.26 Two similar and equal charges repel each
other with force of 1.6 N, when placed 3m q 1 q 1
(C) 2 (D)
apart. Strength of each charge is- 4m  0L3 2 16  0mL3
(A) 40 C (B) 20C
(C) 4C (D) 2C Q.32 Two small balls having equal positive charge Q
(Coulomb) on each are suspended by two
Q.27 There are two charges +1 micro-coulomb and insulating strings of equal length 'L' metre, from
+5 micro-coulomb, the ratio of force on them a hook fixed to a stand. The whole set up is
will be– taken in a satellite in to space where there is
(A) 1043 (B) 1 : 1 no gravity (state of weight lessness) Then the
(C) 10º (D) 10-43 angle () between the two strings is -

Questions
(A) 0º (B) 90º
based on superposition principle (C) 180º (D) 0º <  < 180º

Q.28 A charge Q is divided in two parts Q1 and Q2

and these charges are placed at distance R. Q.33 ABC is a right angle triangle AB=3cm,
there will be maximum repulsion between BC=4cm charges + 15, +12, -12 esu are
them, when- placed at A, B and C respectively. The
(A) Q2 = ( Q/R), Q1 = Q – (Q/R) magnitude of the force experienced by the
(B) Q2 = (Q/3), Q1 = (2Q/3) charge at B in dyne is-
(C) Q2 = (Q/4), Q1 = (3Q/4) (A) 125 (B) 35
(D) Q1 = Q2 = Q/2 (C) 22 (D) 0

Q.29 The three charges each of 5 × 10–6 coloumb Q.34 Equal charges of each 2C are placed at a
are placed at vertex of an equilateral triangle point x = 0, 2, 4, and 8 cm on the x-axis. The
of side 10cm. The force exerted on the force experienced by the charge at x=2 cm is
charge of 1 C placed at centre of triangle
equal to -
in newton will be
(A) 13.5 (B) zero (A) 5 Newton (B) 10 Newton
(C) 4.5 (D) 6.75 (C) 0 Newton (D) 15 Newton

Q.30 A point charge q1 exerts a force F upon Q.35 Three equal charges (q) are placed at corners
another charge q2. If one other charge q3 be of a equilateral triangle. The force on any
placed quite near to charge q2, then the froce charge is-
that charge q1 exerts on the charge q2 will
be Kq2
(A) Zero (B) 3
(A) F (B) >F a2
(C) < F (D) zero Kq2 Kq 2
(C) (D) 3 3
3a 2 a2
Q.31 A mass particle (mass = m and charge = q)
is placed bewteen two point charges of Q.36 Two identical charges of charge (q) and
charge q separtion between these two charge placed at (-a,0) and (a, 0). Same nature
is 2L. The frequency of oscillation of mass charge particle is placed at origin. It executes
particle, if it is displaced for a small distance
S.H.M. If it is displaced -
along the line joining the charges–
(A) In x-direction
q 1 q 4 (B) In y-direction
(A) 2 (B) 2
m  0L3 m  0L3 (C) at an angle of 45º from the x-axis
(D)along perpendicular to the plane.
Q.37 Two equal negative charge (-q) are fixed at the Q.42 If Q =2 coloumb and f orce on it is
points (0, a) and (0, –a) on the y-axis. A F=100 newtons , Then the value of field
positive charge (Q) is released from rest at the intensity will be -
point (2a, 0) on the x-axis. The charge Q will - (A) 100 N/C (B) 50 N/C
(A) execute simple harmonic motion about the (C) 200 N/C (D) 10 N/C
origin.
(B) move to the origin and remains at rest Q.43 Four equal but like charge are placed at four
(C) move to infinity corners of a square. The electric field intensity
at the center of the square due to any one
(D) execute oscillatory but not simple
charge is E, then the resultant electric field
harmonic motion
intensity at centre of square will be :
(A) Zero (B) 4E
Q.38 Five point charges, each of value +q coulomb, (C) E (D) 1/2E
are placed on five vertices of a regular hexa-
gon of side L metre. The magnitude of the
force on a point charge of value -q coul. Q.44 Two charges 9e and 3e are placed at a
placed at the centre of the hexagon is - distance r. The distance of the point where
the electric field intensity will be zero is:
kq 2 kq2
(A) (B) 5
L2 L2  r 
(A)   from 9e charge

kq2  1 3 
(C) 3 (D) Zero
L2
 r 
Questions
(B)   from 9e charge

based on Electric Field  1  1/ 3 

 r 
Q.39 A pendulem bob of mass 80mg and carrying a (C)   from 3e charge

 1 3 
charge of 2 × 10–8 coul. is at rest in a horizontal
uniform electric field of 20,000 V m–1. Find the  r 
tension in the thread of pendulum - (D)   from 3e charge.

 1  1/ 3 
(A) 8.8 × 10-2 N (B) 8.8 × 10-3 N
(C) 8.8 × 10-4N (D) 8.8 × 10-5 N
Q.45 A proton is first placed at A and then at B
between the two plates of a parallel plate
Q.40 Two charges 4q and q are placed 30 cm. capacitor charged to a P.D. of V volt as
apart. At what point the value of electric field shown. Then force on proton at A is-
will be zero +
+
B --
-
(A) 10 cm. away from q and between the + -
+
charge + A -
+ -
(B) 20 cm. away from q and between the + -
+
+ -
charge
(C) 10 cm. away from q and out side the line (A) more than at B
joining the charge.
(B) less than at B
(D) 10 cm. away from 4q and out side the
(C) equal to that at B
line joining them.
(D) nothing can be said
Q.41 Unit of electric field intensity is newtons/
Q.46 An electric field can deflect -
coulomb. The other unit of this can be
(A) Vm . (B) Vm 2 (A) X-rays (B) Neutrons
(C) V/m (D) V/m 2 (C)  -particles (D)  - rays
Q.47 Which one of the following relations is correct Q.52 In electric f ield, a 6.75  C charge
(A) 1 N/C = 108 Volt / m experiences 2.5 N force, when placed at
(B)1 N/C = 10–6 V/m distance of 5m from the origin. Then potential
(C)1 N/C = 1 V/m gradient at this point will be- (in M.K.S.)
(A) 5.71 × 105 (B) 3.71 × 105
(D)1 N/C = 10–8 V/m
(C) 18.81 × 105 (D) 1.881 × 105

Q.48 If mass of the electron = 9.1 × 10–31 Kg. Charge

on the electron = 1.6 × 10–19 coulomb and Q.53 A ring of radius (R) carries a uniformly
g = 9.8 m/s2. Then the intensity of the electric distributed charge + Q. A point charge-q is
field required to balance the weight of an placed on the axis of the ring at a distance 2R
electron is- from the centre of the ring and released from
rest . The particle
(A) 5.6 × 10-9 N/C (B) 5.6 × 10–11 N/C
(A) Becomes in rest condition immediately.
(C) 5.6 × 10–8 N/C (D) 5.6 × 10–7 N/C
(B) Executes simple harmonic motion
(C) Motion is not SHM
Q.49 Six charges +Q each are placed at the (D) Come at the centre of ring immediately.
corners of a regular hexagon of side (a), the
electric field at the centre of hexagon is- Q.54 A small circular ring has a uniform charge
distribution. On a far-off axial point distance x
1 6Q 2 from the centre of the ring, the electric field is
(A) Zero (B) . 2
4 0 a proportional to-
(A) x–1 (B) x–3/2
1 Q2 1 6Q 2 (C) x–2 (D) x5/4
(C) . (D) 4  .
4 0 a 2 0 a 2
Questions
based on Potential and potential difference
Q.50 Two charged spheres A and B are charged
with the charges of +10 and +20 coul. Q.55 When charge of 3 coulomb is placed in a
respectively and separated by a distance of Uniform electric field , it experiences a force
80cm. The electric field at a point on the line of 3000 newton, within this field, potential
joining the centres of the two sphers will be difference between two points separated by
zero at a distance from sphere A. a distance of 1 cm is-
(A) 20 cm (B) 33 cm (A) 10 Volt (B) 90 Volt
(C) 55 cm (D) 60 cm. (C) 1000 Volt (D) 3000 Volt.

Q.51 Four charges +q, +q, –q and –q are placed Q.56 A uniform electric field having a magnitude
respectively at the corners A, B, C and D of E0 and direction along positive x-axis exists.If
a square of side (a), arranged in the given the electric potential(V) is zero at x = 0 then
order. Calculate the intensity at (O) the centre its value at x = + x will be-
of the square . (A) Vx = x E0 (B) Vx = –x.E0
(C) Vx = x2 E0 (D) Vx = x2 E0
4 0 .a 2 4 2q
(A) (B)
4 2q 4 0 .a 2
Q.57 The dimensions of potential difference are -
(A) ML2T –2Q–1 (B) MLT–2Q–1
 0 .a 2
(C) (D) 4 2q (C) MT–2Q–2 (D) ML2 T –1 Q –1
4 2q
 0 .a 2
Q.58 Three equal charges are placed at the three (A) 2.7 × 103 V (B) 1.52 × 105 V
corners of an isosceles triangle as shown in (C) 1.3 × 103 V (D) – 1.52 × 105 V
the figure. The statement which is true for
electric potential V and the field intensity E
at the centre of the triangle is- Q.64 In a region where E = 0, the potential (V)
q varies with distance r as-
1
(A) V
O r
(B) V  r
q q 1
(C) V
r2
(A) V = 0, E = 0 (B) V = 0, E  0
(D) V = const. independent of (r)
(C) V  0 , E =0 (D) V  0, E  0

Q.59 1 e.s.u. of potential is equal to-  10 

Q.65 Charges of +   × 10–9 are placed at each
(A) 1/300 volt (B) 8 ×1010 volt  3 
of the four corners of a square of side 8cm.
(C) 300 volt (D) 3 volt
The potential at the intersection of the diago-
nals is
Q.60 The earth's surface is considered to be at -
(A) 150 2 Volt (B) 1500 2 Volt
(A) Zero potential
(C) 900 2 Volt (D) 900 Volt
(B) Negative Potential
(C) Infinite Potential
Q.66 An equipotential surface is that surface -
(D) Positive Potential
(A) On which each and every point has the
same potential
Q.61 Electric potential is a -
(B) Which has negative potential
(A) Vector quantity
(B) Scalar quantity (C) Which has positive potential
(D) Which has zero potential
(C) Neither vector Nor scalar
(D) Fictious quantity
Q.67 The surface of a conductor -
Q.62 The electric potential V at any point (x, y, z)
(A) is a non-equipotential surface
in space is given by V = 4x2 volt. The electric
(B) has all the points at the same potential
field E in V/m at the point (1, 0, 2) is -
(A) +8 in x direction (B) 8 in –x direction (C) has different points at different potential
(C) 16 in + x direction (D) 16 in –x direction (D) has at least two points at the same
potential
Q.63 ABC is equilateral triangle of side 1m.
Charges are placed at its corners as shown in
fig. O is the mid- point of side BC the Q.68 The electron potential (V) as a function of
potential at point (O) is- distance (x) [in meters] is giv en by
A 6 c V = (5x2 + 10 x-9)Volt.
The value of electric field at x =1m would be-
(A) 20 Volt/m (B) 6 Volt/m
(C) 11 Volt/m (D) –23 Volt/m
2 c 3 c
B C
O
Q.69 Some equipotential lines are as shown is fig. Q.73 Three charges are placed as shown in fig if
E1, E2 and E3 are the electric fields at the electric potential energy of system is
points 1, 2 and 3 then - zero, then Q : q-

–q Q –q
1   
2 3 r r

Q 2 Q 2
70V (A)  (B) 
60V q 1 q 1
50V 40V 30V 20V

(A) E1 = E2 = E3 Q 1 Q 1
(C)  (D) 
q 2 q 4
(B) E1 > E2 > E3
(C) E1 > E2, E2< E3
Q.74 If a unit charge is taken from one point to
(D) E1 < E2 < E3
another over an equipotential surface then-
(A) Work is done on the charge
Q.70 Three charges 2q, -q, -q are located at the (B) Work is done by the charge
vertices of an equilateral triangle. At the
(C) Work on the charge is constant
circum center of the triangle.
(D) No work is done
(A) The field is zero but potential is not zero.
(B) The field is non-zero but the potential is
zero. Q.75 In an electric field the work done in moving a
(C) Both, field and potential are zero. unit positive charge between two points is the
measures of-
(D) Both, field and potential are non- zero
(A) Resistance
(B) Potential difference
Electric potential energy and (C) Intensity of electric field
work done (D) Capacitance

Q.76 State which one of the following is correct ?

Q.71 A point positive charge of Q' units is moved (A) Joule = Coulomb × Volt
round another point positive charge of Q units (B) Joule = Coulomb / Volt
in circular path. If the radius of the circle r is
(C) Joule = Volt / Ampere
the work done on the charge Q' in making
(D) Joule = Volt × Ampere
one complete revolution i -

Q QQ' Q.77 One electron volt (eV) of energy is equal to -

(A) (B)
4 0 r 4 0 r
(A) 1.6 × 10–12 ergs
(B) 4.8 × 10–10 ergs.
Q'
(C) 4  r (D) 0 (C) 9 × 1011 ergs.
0
(D) 3 × 109 ergs.
Q.72 A proton is projected with velocity 7.45 × 105
m/s towards an another proton which is at Q.78 The K.E. in electron Volt gained by an  -
rest. The minimum approach is particle when it moves from rest at point
where its potential is 70 to a point where
(A) 10–12 m (B) 10–14 m
–10
potential is 50 volts, is -
(C) 10 m (D) 10–8m
(A) 20 eV (B) 20 MeV.
(C) 40 eV (D) 40 MeV.
Q.79 A  - particle moves towards a rest nucleus, Q.83 Which of the following statements concerning
if kinetic energy of  -particle is 10 MeV and the electrostatics is correct-
atomic number of nucleus is 50. The closest (A) electric line of force never intersect each
approach will be – other
(A) 1.44 × 10–14 m (B) 2.88 × 10–14 m (B) electric lines of force start from positive
(C) 1.44 × 10 –10 m (D) 2.88 × 10–10 m charge and end at the negative charge
(C) electric lines of force start or ends
Q.80 Point charge (q) moves form point (P) to point perpendicular to the surface of a charged
(S) along the path PQRS as shown in fig. in metal.
a uniform electric field E. Pointing coparallel (D) all of the above
to the positive derection of the x-axis. The co-
ordinates of the points P,Q,R and S are
Q.84 When no charge is confined with in the
(a, b, 0), (2a, 0, 0), (a, –b, 0) and (0, 0, 0)
respectively. The work done by the field in the Gauss’s surface, it implies that-
above process is given by the expression (A) E = 0
E  
(B) E and ds are parallel
P
 
S Q (C) E and ds are mutually perpendicular
 
R (D) E and ds are inclined at some angle

(A) q E q (B) –q E a
Q.85 If electric field flux coming out of a closed
(C) q E a 2 (D) qE 2a
2
 b2  surface is zero, the electric field at the surface
will be-
Q.81 Two identical thin rings, each of radius R (A) zero
metres, are coaxially placed at a distance (R) (B) same at all places
metres apart. If Q1 coul and Q2 coul are (C) dependent upon the location of points
respectively The charges uniformaly spread (D) infinites
on the two rings. The work done in moving a
charge (q) from the centre of one ring to that Q.86 If three electric di-poles are placed in some
of other is - closed surface, then the electric flux emitting
(A) zero from the surface will be-
 
q(Q1  Q 2 ) 2 1
(A) zero
(C) negative
(B) positive
(D) None
(B)
 2.4 R
0

q 2 (Q1  Q2 ) Q.87 For which of the following fields, Gauss’s law

(C) is valid-
4 0 R
(A) fields following square inverse law
(B) uniform field
(D)

q(Q1  Q 2 ) 2 1  (C) all types of field
 2.4 R
0
(D) this law has no concern with the field

Questions Q.88 The electric f lux coming out of the

based on Electric flux and Gauss laws equi-potential surface is-
(A) perpendicular to the surface
Q.82 The tangent drawn at a point on a line of (B) parallel to the surface
electric force shows the- (C) in all directions
(A) intensity of gravity field (D) zero
(B) intensity of magnetic field
(C) intensity of electric field
(D) direction of electric field
Q.89 A charge of Q coloumb is located at the
centre of a cube. If the corner of the cube is
(C)
taken as the origin, then the flux coming out
from the faces of the cube in the direction of
X- axis will be-
(A) 4 Q (B) Q/6 0
(C) Q/3 0 (D) Q/4 0
(D)
Q.90 A rectangular surface of 2 metre width and 4
metre length, is placed in an electric field of
intensity 20 newton/C, there is an angle of
60º between the perpendicular to surface and
electrical field intensity. Then total flux emitted Q.95 In fig. shown the electric lines of force
from the surface will be- (In Volt- metre) emerging from a charged body. If the electric
(A) 80 (B) 40 fields at A and B are E A and E B are
(C) 20 (D) 160 respectively, If the distance between A and B
is r then -
(A) EA> EB
Q.91 A charge q is inside a closed surface and
(B) EA<EB
charge – q is outside. The out going electric r
(C) EA= EB A B
flux is-
(D) EA= (EB)/r2
(A) – q/ 0 (B) zero
(C) q/ 0 (D) 2q/ 0
Questions
based on Application of Gauss law
Q.92 If the electric field is uniform, then the electric Q.96 Three charges q1 = 1 c , q2 =2 c and
lines of forces are-
q3 = –3 c and four surfaces S1, S2, S3 and
(A) Divergent (B) Convergent S4 are shown. The flux emerging through
(C) Circular (D) Parallel surface S2 in N-m2 / C is -

Q.93 Electric lines of forces-

(A) Exist everywhere s3
q1 q3
(B) Are imaginary q2
s1
s2
(C) Exist only in the immediate vicinity of s4
electric charges
(D) None of the above (A) 36  × 103 (B) –36  × 103
(C) 36  × 109 (D) –36  × 109
Q.94 Which one of the following diagrams shows
the correct lines of force ? Q.97 A surface enclosed an electric dipole, the flux
through the surface is-
(A) (A) Infinite (B) Positive
+ (C) Negative (D) Zero

Q.98 Total flux coming out of some closed surface

is -
(A) q/0 (B) 0/q
+ q
(B)
(C) q0 (D) 0
Q.99 A square of side 20cm. is enclosed by a Q.105 A cubical box of side 1m is immersed a
surface of sphere of 80 cm. radius . square uniform electric field of strength 104 N/C. The
and sphere have the same centre. four charges flux through the cube is-
+2 × 10–6 c, –5 × 10–6 c, –3 × 10–6 c, (A) 104 (B) 6 × 104
+6 × 10–6c are located at the four corners of (C) 2 × 104 (D) Zero
a square, Then out going total flux from
spherical surface in N-m 2/c will be
Q.106 A charge (q) is located at the centre of a
(A) zero (B) (16) × 10–6 cube. The electric flux through any face of the
(C) (8) × 10 –6 (D) (36 ) × 10–6 cube is-

q q
Q.100 The flux emerging out from any one face of (A)  (B) 2 
the cube will be - o o

q q q q
(A) 6 (B) 3 (C) (D)
4 o 6 o
0 0

Q.107 A large isolated metal sphere of radius (R)

q q
(C)  (D) 4 carries a fixed charge. A small charge is
0 0 placed at a distance (r) from its surface
experiences a force which is -
Q.101 A charge Q is distributed over two concentric (A) Proportional to R
hollow spheres of radii (r) and (R) > (r) such (B) Independent of R and
the surface densities are equal. Find the (C) Inversely proportional to (R+r)2
potential at the common centre. (D) inversely proportional to r2
Q (r  R) Q(R 2  r )2
(A) 4  (B) Q.108 A hollow sphere of charge does not produce
0 (R  r )2 4 0 (r  R) an electric field at any-
Q(r  R ) (A) Interior point
(C) 2 2 (D) none of these (B) Outer point
4 0 (R  r )
(C) Surface point
Q.102 The electric field inside a spherical shell of (D) None of the above
uniform surface charge density is -
(A) Zero Q.109 A spherical conductor of radius 50 cm has a
surface charge density of 8.85 x 10-6 C/m2 .
(B) Constant, different from zero
The electric field near the surface in N/C is-
(C) Proportional to the distance from the centre
(A) 8.85 × 10–6 (B) 8.85 × 106
(D) None of the above (C) 1 × 106 (D) Zero

Q.103 The earth had a net charge equivalent to

1 electron/m 2 of surface area of radius Q.110 A hollow metal sphere of radius 5cm is
6.4 × 106 m. Its potential would be- charged such that the potential on its surface
is 10V. The potential at the centre of the
(A) + 0.12 volt (B) – 0.12 volt
(C) + 1.2 volt (D) – 1.2 volt sphere is -
(A) 0V
(B) 10V
Q.104 The electric potential at the surface of an
atomic nucleus (Z = 50) of radius 9 × 10–15 m (C) Same as at point 5cm away from the
surface
is -
(D) Same as at point 25cm away from the
(A) 80V (B) 8 × 106 V
surface
(C) 8 × 104 V (D) 8 × 102 V
Q.111 A solid conducting sphere having a charge Q Q.115 An electric dipole consists of two opposite
is surrounded by an uncharged concentric charges each of magnitude 1 × 10 –6 C
conducting hollow spherical shell Let the separated by a distance 2cm. The dipole is
potential difference between the surface of the placed in an external field of 10 × 105N/C.
solid sphere and that of the outer surface of The maximum torque on the dipole is -
the hollow shell be V. If the shell is now given (A) 0.2 × 10–3 N-m (B) 1.0 × 10–3 N-m
a charge of 3Q the new potential difference
(C) 2 × 10-3 N-m (D) 4 × 10–3 N-m
between the same two surfaces is
(A) V (B) 2V
Q.116 The ratio of the electric field due to an electric
(C) 4V (D) –2V dipole on its axis and on the perpendicular
bisector of the dipole is-
Q.112 The electric field intensity at a point located (A) 1 : 2 (B) 2 : 1
at distance r (r < R) from the center of a (C) 1 : 4 (D) 4 : 1
spherical conductor (radius R) charged Q will
be - Q.117 The region surrounding a stationary electric
(A) kQR/r3 (B) kQr/R3 dipole has-
(C) kQ/r2 (D) zero. (A) electric field only
(B) magnetic field only
Q.113 The dependence of electric potential V on (C) both electric and magnetic fields
the distance 'r' from the centre of a charged (D) neither electric nor magnetic field
spherical shell is shown by.

V V Q.118 The electric potential at a point due to an

electric dipole will be.
(A) (B)    
p. r p. r
(A) k (B) k
r r r 3
r2

V    
V k( p  r )
(C) k ( p  r ) (D)
(C) (D) r r2

r r

Questions
based on Electric dipole

Q.114 If an electric dipole is kept in a unifrom

electric field , Then it will experience
(A) a force
(B) a couple and mover
(C) a couple and rotates
(D) a force and moves.
 LEVEL # 2
Q.1 5x105 lines of electric flux are entering in a Q.7 Two small balls having equal positive charge
closed surface and 4x105 liner come out of Q on each are suspended by two insulating
the surface the charge enclosed by the strings at equal length L meter, from a hook
surface is - fixed to a stand. The whole set up is taken
(A) 00.885 × 10–6C (B) 8.85 × 10–6C in a satellite into space where there is no
–7
(C) –8.85 × 10 C (D) 8.85 × 10–8C gravity. Then the angle  between two strings
and tension in each string is-
Q.2 A cylinder of radius (R) and length (L) is
placed in a uniform electrical field (E) parallel kq2
kq 2
to the axis of the cyclinder . the total flux for (A) 0, (B) ,
the surface of the cylinder is given by - L2 2 L2

(A) 2R2E (B) R2E

kq2  kq 2
(C) , (D) 2 , 2
R 2  R 2 4 L2 2L
(C) (D) zero
E
Q.8 The magnitude of the electric field strength
Q.3 A hemisphere (radius R) is placed in electric (E) such that an electron placed in the field
field as shown in fig. Total outgoing flux is - would experience an electrical force equal to
its weight is [ assume g = 10 m/see2 ]
E (A) 5.68 × 10–11 N/ Coul. Vertically up.
R (B) 5.68 × 10–11 N/ Coul. Vertically down.
(C) 5.68 × 10–10 N/ Coul. Vertically up.
(A) R2E (B) 2R2E (D) 5.68 × 10–10 N/ Coul. Vertically down.
(C) 4R2E (D) (R2E)/2
Q.9 Electric potential in an electric field is given
as V= K/r, (K being constant), if position
Q.4 Three identical charges each of 1 C are

kept on the circumference of a circle of radius vector r  2 î  3 ĵ  6k̂ then electric field will
1 metre forming equilateral triangle. The
electric intensity at the center of the circle in be
N/C is -
(A) 9 × 103 (B) 13.5 × 103 (2 î  3 ĵ  6k̂ )K (2 î  3 ĵ  6k̂ )K
(A) (B)
(C) 27 × 103 (D) Zero 243 343

Q.5 The number of electrons,falling on spherical (3 î  2 ĵ  6k̂ )K (6 î  2 ĵ  3k̂ )K

(C) (D)
conductor (radius = 0.1 m) to produce.036 243 343
N/C electric field at the surface of conductor,
is-
Q.10 At any point ( x,0,0) the electric potential V
(A) 2.7 × 105 (B) 2.5 × 105
(C) 2.6 × 105 (D) 2.4 × 105  1000 1500 500 
is   2  3  volt, then electric
 x x x 
Q.6 A particle of mass 6 g carrying a charge of
10-9 C, is placed in the electric field of field at x = 1 m -
strength E= 6x105 V/m, the acceleration
(A) 5500( ĵ  k̂ ) V / m (B) 5500 î V / m
acquired by the particle is-
(A) 102 m/sec 2 (B) 105 m/sec2
3 2 5500 5500
(C) 10 m/sec (D) 1020 m/sec2 (C) ( ĵ  k̂ ) V / m (D) ( î  k̂ ) V / m
2 2
Q.11 The electric field at the surface of a charged Q.16 A charged particle of mass (m) is kept in
spherical conductor is 10 KV/m. The electric equilibrium in the electric field between the
field at a distance equal to the diameter from plates of millikan oil drop experiment. If the
its centre will be - direetion of the electric field between the plate
(A) 2.5 V/m (B) 2.5 KV/m is reversed. then acceleration of the charged
(C) 5.0 KV/m (D) 5.0 V/m particle will be-
(A) Zero (B) g /2 (C) g (D) 2g
Q.12 Potential difference between centre and the
surface of a sphere of radius R with uniform Q.17 Two conducting spheres of radii r1 and r2 are
charge density  with in it will be equally charged. The ratio of their potentral is-
(A) r12 / r22 (B) r22 / r12
R 2 R 2
(A) (B) (C) r1 / r2 (D) r2 / r1
6 0 4 0

R 2 Q.18 Two identical small balls, each of mass , are

(C) zero (D) suspended by two light inelastic conducting
2 0
threads each of length l from the same fixed
point support.If the distance (d) between two
Q.13 An Electron is sitvated 3x10-9 m from one balls is very less the d is equal to-
- particle and 4x10 -9 m from another 1/ 3 2/ 3
 2kq2   2kq 2 
- particle . The magnitude of force on the (A)   (B)  
mg  mg 
electron , when two  - particles are    
5×10-9 m apart is - 2/3
 kq2 
(A) 5.64 × 10–11 N (B) 56.4 × 10–11 N. (C)  
 (D) none of these
(C) 0.564 × 10 –11 N (D) 564 × 10–11 N.  2mg 

Q.14 Two large metal plates each of area (A) carry Q.19 A metal sphere A of radius R has a charge
charger +q and -q and face each other. the of Q on it .The field at a point B outside the
plates are separated by a small distance (d) sphere is E. Now another sphere of radius
the electric field between the plates would be R having a charge -3Q is placed at point B.
2q qA The total field at a point mid-way between A
(A)  A (B)  A and B due to both sphere is-
0 0
(A) 4E (B) 8E
q A (C) 12E (D) 16E
(C)  A (D) q 
0 0
Q.20 Two similar rings P and Q ( radius = 0.1 mt )
Q.15 Two parallel plates of infinite dimensions are are placed co-axially at a distance 0.5
uniformly charged. The surface charge density mt.apart .The charge on P and Q is 2C and
on one is A will on the other is B ,field 4C respectively. Work done due to move a
intensity at point C will be- 5C charge from centre of P to the center of
D Q is-
+ + + + + + + + (A) 1.28 J (B) 0.72 J
A  A
(C) 0.144 J (D) 1.44 J
C
B B
- - - - - - Q.21 A uniformly charged rod with charge per unit
length  is bent in to the shape of a
(A) Proportional to( A – B ) semicircle of radius R. The electric field at
the centre is -
(B) Proportional to( A + B )
(C) Zero 2k k
(A) (B)
(D) 2A R 2R
(C) Zero (D) None
Q.22 A thin stationary ring of radius 1 m has a Q.28 In Millikan's oil drop experiment an oil drop
positive charge 10 µC uniformly distributed carying a charge Q is held stationary by a
over it. A particle of mass 0.9 gm and having potential difference 2400V between the
a negative charge of 1 µC is placed on the plates. To keep a drop of half the radius
axis at a distance of 1 cm from the centre of stationary the potential difference had to be
the ring and released then time period of made 600 V. What is the charge on the
oscillation of particle will be– second drop
(A) 0.6 sec. (B) 0.2 sec.
Q Q 3Q
(C) 0.3 sec. (D) 0.4 sec. (A) (B) (C) Q (D)
4 2 2

Q.23 Three point charge -q, +q and -q are placed Q.29 As per this diagram a point charge +q is
along a straight line at equl distances( say r placed at the origin O. Work done in taking
meter) Electric potential energy of this another pont charge –Q from the point A [co-
system of charges will be if +q charge is in ordinates (0, a)] to another point B [co-
the middle- ordinates (a,0)] along the straight path AB is
Y
 3q2  8q2
(A) (B) A
4 0 r 3 0 r

 3q2  q2
(C) (D)
8 0 r 8 0 r

O B X
Q.24 Four equal charges of charge q are placed at
corner of a square of side a. Potential energy   qQ 1 
of the whole system is- (A) Zero (B)  4  2  2a
 0 a 

4kq 2 4kq 2  1   qQ 1  a  qQ 1 
(A) (B) a 1   (C)  4 2  (D)  4  2  2a
a  2 2  0 a  2  0 a 

1 kq2 kq 2  1  Q.30 The electric field due to an electric dipole at

(C) (D)  4   a distance r from its centre in axial position
2 2 a a  2 2
is E. if the dipole is rotated through an angle
of 90º about its perpendicular axis, the
Q.25 The potential of a charged drop is v. This is
electric field at the same point will be
divided into n smaller drops, then each drop
will have the potential as ; (A) E (B) E/4 (C) E/2 (D) 2E
(A) n–1v (B) n2/3v. Q.31 Two electric dipoles of moment P and 64 P
(C) n3/2v (D) n–2/3 v are placed in opposite direction on a line at
a distance of 25 cm. The electric field will be
Q.26 8 small droplets of water of same size and zero at point between the dipoles whose
same charge form a large spherical drop. The distance from the dipole of moment P is
potential of the large drop, in comparision to
25
potential of a small drop will be - (A) 5 cm (B) cm
(A) 2 times (B) 4 times 9
(C) 8times (D) same 4
(C) 10 cm (D) cm
13
Q.27 Three chargges +3q , +q and Q are placed 
on a straight line with equal separation . In Q.32 When an electric dipole P is placed in a
order to make the net force on q to be zero, uniform electric field E then at what angle
 
the value of Q will be between P and E the value of torque will be
(A) +3q (B)+2q maximum
(C) -3q (D) -4q (A) 90º (B) 0º (C) 180º (D) 45º
 
Q.33 An electric dipole of moment p placed in a Q.37 A ball of mass 1 g and charge 10–8C moves
 from a point A. where potential is 600 volt to
uniform electric field E has minimum potential
the point B where potential is zero. Velocity
 
energy when the angle between p and E is of the ball at the point B is 20 cm/s. The
velocity of the ball at the point A will be
 3 (A) 22.8 cm/s (B) 228 cm/s
(A) Zero (B) (C)  (D)
2 2
(C) 16.8 cm/s (D) 168 m/s
Q.34 An electric dipole has the magnitude of its
charge as q and its dipole moment is p. It is Q.38 An electric dipole is placed along the x-axis
placed in a uniform electric field E. If its at the origin O.A point P is at a distance of
dipole moment is along the direction of the 20cm from this origin such that OP makes
field, the force on it and its potential energy 
an angle with the x-axis. If the electric
are respectively 3
(A) 2q.E and minimum field at P makes an angle  with the x-axis,
the value of  would be
(B) q.E and p.E
(C) Zero and minimum   1 3 
(A) (B) 3  tan  2 
(D) q.E and maximum 3  

2 1 3 
Q.35 Two opposite and equal charges 4 × 10–8 (C) (D) tan  2 
3  
coulomb when placed 2 × 10–2 cm away, form
a dipole. If this dipole is placed in an external

electric field 4 × 108 newton/coulomb, the value Q.39 An electric dipole of moment p is placed
of maximum torque and the work done in normal to the lines of force of electric
rotating it through 180º will be 
intensity E , then the work done in deflecting
(A) 64 × 10–4 Nm and 64 × 10–4 J
(B) 32 × 10–4 Nm and 32 × 10–4 J it through an angle of 180ºis
(C) 64 × 10–4 Nm and 32 × 10–4 J (A) pE (B) + 2pE
(D) 32 × 10–4 Nm and 64 × 10–4 J (C) – 2pE (D) Zero

Q.36 There is an electric field E in X-direction. If

the work done on moving a charge 0.2C
through a distance of 2m along a line making
an angle 60º with the X-axis is 4.0, what is
the value of E

(A) 3 N/C (B) 4N/C

(C) 5N/C (D) None of these
 LEVEL # 3
Q.1 If an electron enters into a space between the Q.5 In a certain region of surface there exists a
plates of a parallel plate capacitor at an angle 
with the plates and leaves at an angle  to the uniform electric field of 2 × 103 k̂ V/m. A
plates. The ratio of its kinetic energy while rectangular coil of dimensions 10 cm × 20 cm
entering the capacitor to that while leaving will is placed in x-y plane. The electric flux through
be - the coil is -
2 2 (A) Zero (B) 30 V-m
 sin    cos  
(A)   (B)   (C) 40 V-m (D) 50 V-m
 sin    cos  
2 2 Q.6 The electric flux from a cube of edge  is .
 cos    sin  
(C)   (D)   What will be its value if edge of cube is made 2
 cos    sin   and charge enclosed is halved -
(A) /2 (B) 2
Q.2 Force between two identical charges placed at
(C) 4 (D) 
a distance of r in vacuum is F. Now a slab of
dielectric constant K = 4 is inserted between
Q.7 Each of the two point charges are doubled and
these two charges. The thickness of the slab is
their distance is halved. Force of interaction
r/2. The force between the charges will now
becomes n times, where n is -
become -
(A) F/4 (B) F/2 (A) 4 (B) 1
3 4 (C) 1/16 (D) 16
(C) F (D) F
5 9
Q.8 Two point charges repel each other with a force
Q.3 A conducting sphere of radius R is charged to a of 100 N. One of the charges is increased by
potential of V volt. Then the electric field at a 10% and other is reduced by 10%. The new
force of repulsion at the same distance would be-
distance r (>R) from the centre of the sphere
would be - (A) 100 N (B) 121 N
(C) 99 N (D) None of these
RV V
(A) 2 (B)
r r Q.9 A positive point charge q is carried from a point
B to a point A in the electric field of a point
rV R2 V charge +Q at O. If the permittivity of free space
(C) (D) is 0, the work done in the process is given by
R2 r3
(where a = OA and b = OB) -
Q.4 The variation of electric potential with distance qQ  1 1  qQ  1 1 
(A)    (B)   
from a fixed point is shown in figure. What is 4 0  a b  4 0  a b 
the value of electric field at x = 2m -
qQ  1 1  qQ  1 1 
(C)    (D)   
2
4 0 a b2  4 0 a 2
b2 

Q.10 A spherical charged conductor has  as the

surface density of charge. The electric field on
its surface is E. If the radius of the sphere is
doubled keeping the surface density of charge
unchanged, what will be the electric field on the
surface of the new sphere -
(A) Zero (B) 6/2 E E
(C) 6/1 (D) 6/3 (A) (B)
4 2
(C) E (D) 2 E
Q.11 Three equal and similar charges are placed at Q.16 The electric field strength due to a ring of radius
(–a, 0, 0), (0, 0, 0) and (+a, 0, 0). What is the R at a distance x from its centre on the axis of
nature of equilibrium of the charge at the origin- ring carrying charge Q is given by
(A) Stable when moved along the Y-axis
(B) Stable when moved along Z-axis 1 Qx
E = 4  2 2 3/2
(C) Stable when moved along X-axis 0 (R  x )
(D) Unstable in all of the above cases At what distance from the centre will the electric
field be maximum -
Q.12 Two conducting spheres each of radius R carry
(A) x = R (B) x = R/2
charge q. They are placed at a distance r from
each other, where r > 2 R. The neutral point lies (C) x = R/ 2 (D) x = 2R
at a distance r/2 from either sphere. If the
electric field at the neutral point due to either
Q.17 Two conducting spheres of radii r1 and r2 are
sphere be E, then the total electric potential at
charged such that they have the same electric
that point will be -
field on their surfaces. The ratio of the electric
(A) r E/2 (B) r E potential at their centres is -
(C) RE/2 (D) RE
(A) r1 / r2 (B) r1/r2
Q.13 A ring of radius R carries a charge +q. A test (C) r12/r22 (D) None of the above
charge –q0 is released on its axis at a distance
Q.18 Five equal and similar charges are placed at
3 R from its centre. How much kinetic energy
the corners of a regular hexagon as shown in
will be acquired by the test charge when it
the figure. What is the electric field and potential
reaches the centre of the ring -
at the centre of the hexagon -
1 q q0 1 q q0
(A) 4   R (B) 4   2 R
0 0
1 q q0 1 q q0
(C) 4   (D) 4   3 R
0 3R 0

Q.14 Two spheres of radii r1 and r2 are at the same

potentials. If their surface densities of charges 5 q 5 q
be 1 and 2 respectively, then 1/2 - (A) 4    , 4   2
0 0 
(A) r1/r2 (B) r2/r1
1 q 5 q
(C) (r1/r2)2 (D) (r2/r1)2 (B) 4    , 4   2
0 0 

Q.15 A proton and an electron are released infinite 1 q 5 q

(C) 4   2 , 4   
distance apart and the attracted towards each 0  0
other. Which of the following statement about
1 q 1 q
their kinetic energy is true - (D) 4    , 4   2
0 0 
(A) Kinetic energy of electron is more than that
of proton
Q.19 Two point charges Q and –3Q are placed certain
(B) Kinetic energy of electron is less than that distance apart. If the electric field at the location
of proton 
of Q be E , then that at the location of –3Q
(C) Kinetic energy of electron = kinetic energy
will be-
of proton  
(D) None of the above is true as it depending on (A) 3 E (B)  3 E
the distance between the particles  
(C) E / 3 (D)  E / 3
Q.20 A charge +Q at A (See figure) produces electric Q.25 A charge Q is placed at each of two opposite
field E and electric potential V at D. If we now corners of a square. A charge q is placed at
put charges –2Q and +Q at B and C respectively, each of the two opposite corners of the square.
then the electric field and potential at D will be - If the resultant electric field on Q is zero, then -
q
(A) Q   (B) Q  2 2 q
2 2
(C) Q = –2q (D) Q  2 2 q

Q.26 Electric potential is given by :

(A) E and 0 (B) 0 and V V = 6x – 8xy2 – 8y + 6yz – 4z2
Electric field at the origin is -
E V
(C) V (D) and (A)  6 î  8 ĵ (B) 6 î  8 ĵ
2 E and 2 2
2 (C) î  ĵ (D) Zero
Q.21 A and B are two points on the axis and the
perpendicular bisector respectively of an electric Q.27 A hollow conducting sphere of radius R has
dipole. A and B are far away from the dipole and charge (+Q) on its surface. The electric potential
at equal distances from it. The fields at A and B R
within the sphere at a distance r  from the
  3
are E A and EB are respectively such that - centre is -
   
(A) E A  EB (B) E A  2 EB 1 Q
(A) Zero (B)
4  0 r
   1
(C) E A  2 EB (D) E A  EB 1 Q 1 Q
2 (C) (D)
4  0 R 4  0 r2

Q.22 A long string with a charge of  per unit length Q.28 The electric field outside a charged long straight
passes through an imaginary cube of edge . 5000
The maximum possible flux of the electric field wire is given by E   V m 1 . It is radially
r
through the cube will be - inward. The value of VB – VA is -
(A) /0 (B) 2 /0 [Given rB = 60 cm and rA = 30 cm]

(C) 6 2 /0 (A) 5000 loge2 volt (B) 0 V

(D) 3 /0
(C) 2 V (D) 2500 V
Q.23 If a positive charge is shifted from a low-potential
Q.29 A particle has a mass 400 times than that of
region to a high-potential region, the electric
the electron and charge is double than that of a
potential energy -
electron. It is accelerated by 5 V of potential
(A) increases difference. Initially the particle was at rest. Then
(B) decreases its final kinetic energy will be -
(C) remains the same
(D) May increase or decrease (A) 5 eV (B) 10 eV
(C) 100 eV (D) 2000 eV
Q.24 A particle of mass 0.002 kg and a charge 1C
is held at rest on a frictionless horizontal surface Q.30 Two equal positive charges are kept at points A
at a distance of 1m from a fixed charge of 1mC. and B. The electric potential at the points
If the particle is released, it will be repelled. The between A and B (excluding these points) is
speed of the particle when it is at a distance of studied while moving from A to B. The potential-
10m from the fixed charge is -
(A) Continuously increases
(A) 60 ms–1 (B) 75 ms–1
(B) Continuously decreases
(C) 90 ms–1 (D) 100 ms–1
(C) Increases then decreases
(D) Decreases then increases
  Q.35 If the particles are positively charged, which
Q.31 An electron moves with velocity v in x-direction.
An electric field acts on it in y-direction. The particles increased their electrical potential
force on the electron acts in - energy -
(A) X and Z
(A) +ve direction of Y-axis
(B) Y and Z
(B) –ve direction of Y-axis
(C) W, X, Y and Z
(C) +ve direction of Z-axis
(D) Since the electric field is constant none of
(D) –ve direction of Z-axis
the particles increased their electrical
potential energy.
Q.32 Two identical simple pendulums A and B, are
suspended from the same point. The bobs are Statements Type Question :-
given positive charges, with A having more Each of the questions given below consist
charge than B. They diverge and reach of Statement – I and Statement – II. Use
equilibrium, with A and B making angles 1 and the following Key to choose the appropri-
2 with the vertical respectively. Which of the ate answer.
following is correct - (A) If both Statement- I and Statement- II are
(A) 1 > 2 (B) 1 < 2 true, and Statement - II is the correct
(C) 1 = 2 explanation of Statement– I.
(D) The tension in A is greater than that in B (B) If both Statement - I and Statement - II
are true but Statement - II is not the
correct explanation of Statement – I.
Passage Type Question :- (C) If Statement - I is true but Statement - II is
In the diagram (given below) the broken lines false.
represent the paths followed by particles W,X,
(D) If Statement - I is false but Statement - II
Y and Z respectively through the constant field
is true.
E. The numbers below the field represents
meters. Q.36 Statement I : Electrons move away from a
region of lower potential to a region of higher
X potential.
Statement II : Since an e – has negative
charge.

Y Q.37 Statement I : If a point charge q is placed in

front of an infinite grounded conducting plane
W surface, the point charge will experience a force.
Z Statement II : The force is due to the induced
charge on the conducting surface which is at
zero potential.
Q.38 Statement I : Work done in moving a charge
between any two points in an electric field is
independent of the path followed by the charge,
0 1 2 3 4 5
between these points.
Q.33 If the particles begin and end at rest, and all Statement II : Electrostatic forces are non
are positively charged, the same amount of work conservative.
was done on which particles. Q.39 Statement I : Force between two charges
(A) W and Z (B) W, Y and Z decreases when air separating the charges is
(C) Y and Z (D) W, X, Y and Z replaced by water.
Statement II : Medium intervening the charges
Q.34 If the particles started from rest and all are has no effect on force.
positively charge which particles must have been
acted upon by a force other than that produced Q.40 Statement I : The no. of lines of f orce
emanating from 1µC charge in vacuum is
by the electric field.
1.13 × 105.
(A) W and Y (B) X and Z
Statement II : This follow from Gauss's
(C) X,Y and Z (D) W, X,Y and Z theorem in electostates.
 LEVEL # 4
( Question asked in previous AIEEE & IIT-JEE)
SECTION - A Q.5 If the electric flux entering and leaving an
Q.1 When two charges are placed at a distance enclosed surface respectively is 1 and 2, the
apart. Find the magnitude of third charge which electric charge inside the surface will be –
is placed at mid point the line joining the charge.
So that system is in equilibrium - (A) (1 +2)/0 (B) (2 –1)/0
(C) (1 + 2)0 (D) (2 – 1)0
Q Q
(A)  (B)  Q.6 A thin spherical conducting shell of radius R
4 2
has a charge q. Another charge Q is placed at
Q the centre of the shell. The electrostatic potential
(C)  (D) – Q1
3 at a point P a distance R/2 from the centre of
Q.2 On moving a charge of 20 coulombs by 2 cm, the shell is –
2J of work is done, then the potential difference 2Q 2q 2Q q
between the points is – (A) 4 R – 4 R (B) 4 R + 4 R
0 0 0 0
(A) 0.1 V (B) 8 V
(C) 2 V (D) 0.5 V
Q.3 A charged particle q is placed at the centre O of (q  Q ) 2 2Q
(C) 4 0 R (D) 4 R
cube of length L (ABCDEFGH). Another same 0
charge q is placed at a distance L from O. Then
the electric flux through BCFG is – Q.7 Two spherical conductors B and C having equal
radii and carrying equal charges on them repel
each other with a force F when kept apart at
some distance. A third spherical conductor
having same radius as that of B but uncharged
is brought in contact with B, then brought in
contact with C and finally removed away from
both. The new force of repulsion between B and
C is –
q
(A) L (B) zero (A) F/4 (B) 3F/4
4  0
(C) F/8 (D) 3F/8
q q
(C) L (D) Q.8 A charged particle ‘q’ is shot towards another
2  0 3  0 L
charged particle ‘Q’, which is fixed, with a speed
Q.4 Three charges –q1, +q2 and –q3 are placed as ‘v’. It approaches ‘Q’ upto a closest distance r
shown in figure. The x-component of the force and then returns. If q were given a speed of ‘2v’,
on –q1 is proportional to – the closest distances of approach would be –

(A) r (B) 2 r
(C) r/2 (D) r/4
Q.9 Four charges equal to – Q are placed at the
four corners of a square and a charge q is at its
centre. If the system is in equilibrium the value
of q is –
q2 q3 q2 q3 Q Q
(A) 2 + 2 sin  (B) 2 + cos  (A) – (1 + 2 2) (B) (1 + 2 2)
b a b a2 4 4
q2 q3 q2 q3 Q Q
(C) 2 – 2 sin  (D) 2 – cos  (C) – (1 + 2 2) (D) (1 + 2 2)
b a b a2 2 2
Q.10 A charged oil drop is suspended in a uniform Q.14 An electric dipole is placed at an angle of 30º to
field of 3 × 104 v/m so that it neither falls nor a non-uniform electric field. the dipole will
experience –
rises. The charge on the drop will be (Take the
(A) a torque as well as a translational force
mass of the charge = 9.9 × 10–15 kg and g = 10
(B) a torque only
m/s2) –
(C) a translational force only in the direction of
(A) 3.3 × 10–18 C (B) 3.2 × 10–18 C the field
(C) 1.6 × 10–18 C (D) 4.8 × 10–18 C
(D) a translational force only in a directin normal
to the direction of the field
Q.11 A charged ball B hangs from a silk thread S
which makes an angle  with a large charged Q.15 Two insulating plates are both uniformly charged
conducting sheet P, as shown in the figure. The in such a way that the potential difference
surface charge density  of the sheet is between them is V2 – V1 = 20 V. (i.e. plate 2 is
proportional to - at a higher potential). The plates are separated
by d = 0.1 m and can be treated as infinitely
large. An electron is relaeased from rest on the
inner surface of plate 1. What is its speed when
it hits plate 2 ?
(e = 1.6 × 10–19 C, me = 9.11 × 10–31 kg) –

(A) cos  (B) cot 

(C) sin  (D) tan 

Q.12 Two point charges +8q and –2q are located at

x = 0 and x = L respectively. The location of a
point on the x axis at which the net electric field
due to these two point charges is zero is (A) 1.87 × 106 m/s (B) 32 × 10–19 m/s
(C) 2.65 × 106 m/s (D) 7.02 × 1012 m/s
(A) 2 L (B) L/4
(C) 8 L (D) 4 L Q.16 Two spherical conducors A and B of radii 1 mm
and 2 mm are separated by a distance of 5 cm
and are uniformly charged. If the sphere are
Q.13 Two thin wire rings each having a radius R are connected by a conducting wire then in
placed at a distance d apart with their axes equilibrium condition, the ratio of the magnitude
coinciding. The charges on the two rings are of the electric fields at the surfaces of spheres
+q and –q. The potential difference between A and B is –
the centres of the two rings is (A) 2 : 1 (B) 1 : 4
(C) 4 : 1 (D) 1 : 2
(A) QR/40d2
Q.17 An electric charge 10-3 C is placed at the
origin (0,0) of X - Y co-ordinate system. Two
Q 1 1 
(B) 2     points A and B are situated at ( 2 , 2 ) and
R R 2  d2 
0  (2, 0) respectively. The potential difference
between the points A and B will be -
(C) zero
(A) 9 volt (B) zero
Q 1 1 
(C) 2 volt (D) 4.5 volt
(D) 4   R  
0 
 R 2  d2 
 E(r)
Q.18 Charges are placed on the vertices of a

square as shown. Let E be the electric field
and V the potential at the centre. If the
charges on A and B are interchanged with
those on D and C respectively, then r
(B) R
O
q q
A B

-q D C
-q E(r) E(r)

(A) E remains
 unchanged, V changes
(B) Both E and V change

(C) E and V remain unchanged
 (C) (D)
(D) E changes, V remains unchanged r r
O R O R
Q.19 The potential at a point x (measured in m)
due to some changes situated on the x-axis
Q.22 This question contains Statement-1 and
is given by V (x) = 20 /(x 2- 4) volts. The Statement-2. Of the four choices given after the
electric field E at x = 4 m is given by statements, choose the one that best describes
the two statements.
(A) 5/3 Volt/m and in the –ve x direction
(B) 5/3 Voltm and in the +ve x direction Statement-1 :
(C) 10/9 Volt/m and in the -ve x direction For a mass M kept at the centre of a cube of
(D) 10/9 Volt/m and in the +ve x direction side ‘a’, the flux of gravitational field passing
through its sides is 4 GM.
Q.20 If gE and gm are the accelerations due to
gravity on the surfaces of the earth and the and
moon respectively and if Millikan’s oil drop Statement-2 :
experiment could be performed on the two If the direction of a field due to a point source is
surfaces, one will find the ratio (electronic radial and its dependence on the distance ‘r’
charge on the moon/ electronic charge on 1
the earth) to be from the source is given as , its flux through
r2
(A) 1 (B) 0
a closed surface depends only on the strength
(C) gE/gM (D) gM/gE of the source enclosed by the surface and not
on the size or shape of the surface.
Q.21 A thin spherical shell of radius R has charge
Q spread uniformly over its surface. Which (A) Statement-1 is true, Statement-2 is true;
Statement-2 is a correct explanation for
of the f ollowing graphs most closely Statement-1
represents the electric field E (r) produced (B) Statement-1 is true. Statement-2 is true;
Statement-2 is not a correct explanation for
by the shell in the range 0  r < , where r Statement-1
is the distance from the centre of the shell? (C) Statement-1 is true, Statement-2 is false.
(D) Statement-1 is false, Statement-2 is true.
E(r)

Q.23 Statement-1 : For a charged particle moving from

point P to point Q, the net work done by an
electrostatic field on the particle is independent
of the path connecting point P to point Q.
(A) O r Statement-2 : The net work done by a
R
conservative force on an object moving along a
closed loop is zero.
 (A) Statement-1 is true, Statement-2 is true; charge q from the centre of one ring to that
Statement-2 is a correct explanation for of the other is
Statement-1
q(Q 1  Q 2 )( 2  1)
(B) Statement-1 is true. Statement-2 is true; (A) zero (B)
Statement-2 is not a correct explanation for 2 4  0R
Statement-1 q 2 (Q1  Q2 ) q(Q1 / Q 2 )( 2  1)
(C) Statement-1 is true, Statement-2 is false. (C) (D)
4  0R 2 4 0R
(D) Statement-1 is false, Statement-2 is true.
Q.2 The electric potential V at any point x, y, z
Q
Q.24 Let P(r) = r be the charge density in space is given by V = 4x 2 volt / meter2.
R 4
The electric field at the point ( 1m, 0, 2m ) is
distribution for a solid sphere of radius R and (A) 8 V/m (B) 4 V/m
total charge Q. For point 'p' inside the sphere
(C) 16 V/m (D) 4/3 V/m
at distance r1 from the centre of the sphere,
the magnitude of electric field is –
Q.3 Five point charges, each of value + q, are
placed on five vertices of a regular hexagon
Q of side L. The magnitude of the force on a
(A) 0 (B)
4 0 r12 point charge of value – q placed at the centre
of the hexagon is
Qr12 Qr12
(C) (D) Kq 2 Kq 2
4 0 R 4 3 0 R 4 (A) 2 (B)
L 4L2
Kq 2 Kq 2
Q.25 Two points P and Q are maintained at the (C) (D)
2L2 8L2
potentials of 10 V and –4V, respectively. The
work done in moving 100 electrons from P to Q.4 Two point charges + q and –q are held fixed
Q is – at (–d,0 )and (d,0) respectively of a (x,y )
(A) –9.60 × 10–17 J (B) 9.60 × 10–17 J coordinate system , then -
(C) –2.24 × 10–16 J (D) 2.24 × 10–16 J 
(A) The electric field E at all points on the
x-axis has the same direction
Q.26 A charge Q is placed at each of the opposite  
corners of a square. A charge q is placed at (B) E at all points on the Y - axis is along i
each of the other two corners. If the net (C) Work has to be done in bringing a test
electrical force on Q is zero, then Q/q equals – charge from infinity to the origin
(D) The dipole moment is 2qd directed

(A) – 2 2 (B) – 1 along i

1 Q.5 A metallic solid spher is placed in a uniform

(C) 1 (D) –
2 electric field. The lines of force follow the
path(s) shown in figure as

SECTION - B 1 1
Q.1 Two identical thin rings, each of radius R, are 2 2
coaxially placed a distance R apart. If Q1 3 3
and Q2 are 4 4
respectively the charges uniformly spread on (A) 1 (B) 2 (C) 3 (D) 4
the two rings, the work done in moving a
Q.6 An electron of mass m e, initially at rest,
moves through a certain distance in a uniform
 electric field in time t1. A proton of mass (A) Electric field near A in the cavity = electric
mp, also, initially at rest, takes time t2 to field near B in the cavity
move through an equal distance in this
uniform electric field. Neglecting the effect (B) Charge density at A = charge density at B
of gravity, the ratio t2/t 1is nearly equal to (C) Potential at A  potential at B
(D) Total electric field flux through the surface
(A) 1 (B) (mp/m e)1/2 of the cavity is q/0.
(C) (me/mp )1/2 (D) 1836
Q.11 Three charges Q, + q and + q are placed at
Q.7 A nonconducting ring of radius 0.5 m carries
the vertices of a right- angled isosceles
a total charge of 1.11 × 10–10 C distributed
triangle as shown in fig. The net electrostatics
non-uniformly on its curcumference producing
an electric field E everywhere in space. The energy of the configuration is zero if Q is
value of the line integral equal to
l 0  
  E . dl (l = 0 being centre of the ring) in
l 
volts is
(A) +2 (B) –1
(C) –2 (D) zero

Q.8 A charge + q is fixed at each of the point x

= x0, x = 3x 0, x = 5 x0, .......ad inf. on the q  2q
x-axis , and charges –q is fixed at each of (A) (B)
the point x = 2x 0, x = 4x 0, x = 6 x 0,........ad 1 2 2 2
inf. Here x0 is a positive constant. Take the (C) – 2q (D) + q
electric potential at a point due to a charge
Q at a distance r f rom it to be
Q / ( 40r). Then the potential at the origin Q.12 Three positive charges of equal value q are
due to the above system of charges is placed at the vertices of an equilateral triangle
. The resulting lines of force should be
q sketched as in
(A) 0 (B) 8  x In 2
0 0
q In 2
(C)  (D) 4   x
0 0

Q.9 A non-conducting solid sphere of radius R is (A)

uniformly charged. The magnitude of the
electric field due to the sphere at a distance
r from its centre
(A) increases as r increases, for r < R
(B) decreases as r increases, for 0 < r < 
(C) increases as r increases, for R< r < 
(D) is discontinuous at r = R
(B)
Q.10 An ellipsoidal cavity is carved within a perfect
conductor. A positive charge q is placed at
the centre of the cavity . The points A and B
are on the cavity surface as shown in the
figure. Then

(C)
 (D)

 q2 Q
(A) only due Pto
Q.13 A uniform electric field pointing in positive x
- direction exists in a region. Let A be the (B) zero on the Gaussian surface
(C) uniform on the  R surface
OGaussian
U
origin, B be the point on the x-axis at x = +
1 cm and C be the point on the y axis at y (D) due to all
= + 1 cm. Then the potentials at the points T
 S
Q.17 Six charges of equal magnitude are placed
A,B, and C satisfy.
at six corners of a regular hexagon. Find
(A) VA < VB (B) VA > VB
arrangement the charges in order PQRSTU
(C) VA < VC (D) VA > VC
which produce double electric field at centre
as compared to electric field produce by
Q.14 Two equal point charges are fixed at x = – a
and x = + a on the x-axis. Another point single charges +q at R
charge Q is placed at the origin. The change
in the electrical potential energy of Q, when
it is displaced by a small distance x along
the x-axis, is approximately proportional to -

(A) x (B) x2
(C) x3 (D) 1 / x
(A) +++- - - (B) + - + - + -

Q.15 A point charge ‘q’ is placed at a point inside (C) - + + - + - (D) - + + + - -

a hollow conducting sphere. Which of the
following electric lines of force pattern is
Q.18 Three large charged sheets having surface
correct ?
charge density as shown in the figure. The
sheets are placed parallel to XY plane. Then
electric field at point P -
(A) (B) ^
K

Z = 3a P 
Z=a 
(C) (D) Z=0

4 4
(A)  k̂ (B)  k̂
0 0
Q.16 In the given figure , charges q1 and -q1 are
inside a Gaussian surface. Where as charge 2 2
q2 is outside the surface. Electric field on (C)  k̂ (D) –  k̂
0 0
the Gaussian surface will be

Q.19 Consider a neutral conducting sphere. A

positive point charge is placed outside the
 sphere. The net charge on the sphere is then,
q
direction along the negative x-
8 0R 2
(A) negative and distributed uniformly over
the surface of the sphere axis
(B) negative and appears only at the point on (B) The potential energy of the system is
the sphere closest to the point charge zero
(C) negative and distributed non-uniformly over (C) The magnitude of the force between the
the entire surface of the sphere q2
(D) zero charges at C and B is
54 0R 2
q
Q.20 Positive and negative point charges of equal (D) The potential at point O is
12 0R
 a  Q.22 STATEMENT-1
magnitude are kept at  0 , 0 ,  and
 2  For practical purposes the earth is used as a
 a reference at zero potential in electrical
 0,0,  , respectively. The work done by
 2  circuits.

the electric field when another positive point and

charge is moved from (–a, 0, 0) to (0, a, 0) STATEMENT-2
is The electrical potential of a sphere of radius R
with charge Q uniformly distributed on the
(A) positive
Q
(B) negative surface is given by 4 R
0
(C) zero
(A) STATEMENT-1 is True, STATEMENT-2 is
(D) depends on the path connecting the initial
and final positions True; STATEMENT-2 is a correct explanation
for STATEMENT-1
q q
Q.21 Consider a system of three charges , (B) STATEMENT-1 is True, STATEMENT-2 is
3 3
2q True; STATEMENT-2 is NOT a correct
and – placed at point A, B and C,
3 explanation for STATEMENT-1
respectively, as shown in the figure. Take O
to be the centre of the circle of radius R and (C) STATEMENT-1 is True, STATEMENT-2 is
angle CAB = 60º. False
Figure : (D) STATEMENT-1 is False, STATEMENT-2 is
True

Q.23 Three concentric metallic spherical shells of radii

R, 2R, 3R are given charges Q 1, Q 2, Q 3
respectively. It is found that the surface charge
densities on the outer surfaces of the shells are
equal. Then, the ratio of the charges given to
the shells, Q1 : Q2 : Q3 is-
(A) The electric f ield at point O is (A) 1 : 2 : 3 (B) 1 : 3 : 5
 (C) 1 : 4 : 9 (D) 1 : 8 : 18
y

Q.24 A disk of radius a/4 having a uniformly distributed

charge 6C is placed in the x-y plane with its
x
centre at (–a/2, 0, 0). A rod of length ‘a’ carrying
a uniformly distributed charge 8C is placed on
the x-axis from x = a/4 to x = 5a/4. Two point
charges –7C and 3C are placed at (a/4, –a/4, 0)
2C 2C
and (–3a/4, 3a/4, 0) respectively. Consider a (A) (B)
0 0
cubical surface formed by six surfaces x = ± a/2,
10C 12C
y = ±a/2, z = ±a/2. The electric flux this cubical (C) (D)
0 0
surface is-
Q.25 Under the influence of the Coulomb field of
charge +Q, a charge –q is moving around it in
an elliptical orbital. Find out the correct
statement(s) -
(A) The angular momentum of the charge – q is
constant
(B) The linear momentum of the charge –q is
constant
(C) The angular velocity of the charge –q is
constant
(D) The linear speed of the charge –q is constant

Q.26 A solid sphere of radius R has a charge Q

distributed in its volume with a charge density
 = ra, where  and a are constants and r is
the distance from its centre. If the electric field
a t
R 1
r= is times that at r = R, find the value of a.
2 8
 ANSWER KEY

LEVEL # 1
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. D D B A B A D A D D C A A A A C D A C A
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. A B B A C A B D B A A C C B B A D A C A
Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. C B A B C C C B A B B B C C A B A C C A
Q.No. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
Ans. B B D D B A B A C B D A D D B A A C A B
Q.No. 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Ans. B D D C C A A A C A C D B B A B D A A A
Q.No. 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
Ans. C A B B D D C A C B A D B C C B A A

LEVEL # 2
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. C D A D B B C B B B B C A C B D D A D B
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Ans. A A C B D B A B A C A A A C D D C B D

LEVEL # 3
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. B D A A C A D C B C C B B B A C B C C A
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. C D A C B A C A B D B C C C B A A C C A

LEVEL # 4
SECTION-A
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A ns. A A B A D B D D B A D A B A C
Q.No. 16 17 18 19 20 21 22 23 24 25 26
A ns. A B D D A D A A C D A

SECTION-B
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Ans. B A A B D B A D A D B C B B B D C D D C C A
Q.No. 23 24 25
Ans. B A A

Q.26 (2)