OBJECTIVE TYPE QUESTIONS

lt(-.ltlplo aAolell QullstloHs the following best represents the resulting

~In an electric field the Null point is a point, curve? [CTQ]

where
(a) there is no charge.
(b) there is no resul~ant force on the charge
(a)1LJ (b) f
E

0 X-+ I X-+ I
placed at that pomt.
(c) there are less number of lines of force. t
(a) none of the above.
E
(c) o
I
(d) 1
0

2. An electric charge in uniform motion

produces
(a) an electric field only. 8. A charged particle q is placed at the centre
(b) a magnetic field only. 0 of cube of length L(A B C D E F G
H). Another same charge q is placed at a
(c) both electric and magnetic field.
distance L from 0. Then the electric flux
(a) neither electric nor magnetic field. [CTQ]
through ABCD is

,.c1 ~-s:..
3. +Q charge is present at the point A, B, C G
of a equilateral triangle. The intensity of
electric field at the centroid is
Q
(a) k 2 E"""----- -.....J..-_
r
Q2 i.A-L ll>I

(c) Zero (d) k -

r2
(b) zero
4. The electric field required to just support
5
a water droplet of mass 10- g, which has
a charge of 10- 13 C is
1
(a) 107 Nc-1 (b) 9.8 x 103 Nc- 9. If the electric flux entering and leaving an
5 1
(c) 106 Nc-1 (d) 9.8 x 10 Nc- enclosed surface respectively is cj,1 and cj,2 ,
p is placed in the electric charge inside the surface will
5. An electric dipole of moment
be
a uniform electric field E,with p parallel (a) (<!>2 - <1>1)80 (b) (cpl + cp2)/Eo
➔
to E . It is then rotated by an angle 0. The (c) (<!>2 - <1>1)/so (d) (cpl + <!>2) 80
work done is 10. Three positive charges of equal value q
(a) pE sin 0 (b) pE cos 0 are placed at the vertices of an equilateral
(c) pE(l - cos 0) (d) pE(l - sin 0) triangle. The resulting lines of force should

(b).
6. A charge q is placed at the centre of a cube be sketched as in: [CTQ]
. of side a. The electric flux through any one
face of the tube is ~
(a) .!L (b) ...!L (a)~
Eo 3Eo

(c) .!L
6£0
(d) 6q
Eo

7. 1\vo identical point charges are placed at

a separation of /. P is a point on the line
joining the charges, at a distance x from
(c)* (d)
0 .

any one charge. The field at P is E. E is 11. A met • point charge 'q'
kept · Ml'll'ttv. f the
plotted against x for values ofx from close
follo .
to zero to slightly less than /. Which of
the elec
 ~
15. A wo ode n blo ck per fo~
. . 1 ms SfI1\• on
f:nct lon ess sur fac e wit h fi
The blo ck car ries a cha rge
v1
requenc:y, va
'
[
(a) ~ (b) ~ +Q on· o·
surface. If now a uniform ectr1.c field Its
el
~
. . th h £
1s switched-on as sho wn
the block wil l be ' en t e S1-I1,t of
(c) (d) _, .
E

+Q ~
12. Six charges of equ al magnitude, 3 positive
and 3 negative are to be placed on PQ RST U
I t:': °°0 00 00 00 00 ~
(a) of the sam e freq uen cy and with
.
cor ner s of a reg ula r hexagon, such that shifted
mea n position.
field at the centre is double that of wha t it
would have bee n if only one +ve charge (b) of the sam e freq uen cy and with th
mea n pos itio n e sarne
is pla ced at R. Wh ich of the following
h'
(c) of cha nge. d. freq uen cy and with s tfted
arra nge men t of charge is possible for P,
Q, R, S, T and U respectively. [CTQ] mea n pos1t1on.
p Q (d) of cha nge.d. frequency and with the same

UQR mea n position.

16. An electric dipole is placed at an angl
e of
30° to a non-uniform electric field. The
(a) + ' +, +, -, -, - (b) -, + , +, +, -, - dipole wil l experience.
(d) + ' -, +, -, +, - (a) a tran slat iona l force only in the direc
tion
(c) -, + ' +, -, +, -
of the field
13. A tiny spherical oil dro p car ryin g a net tion
(b) a tran slat iona l force only in a direc
cha rge q is bal anc ed in stil l air wit h a
nor mal to the direction of the field
vertical uni form electric field of stre ngt h force
d (c) a torq ue as well as a translational
Sl7t xIO ' Nc-1• Wh en the field is switche
7 (d) a torq ue only
off, the dro p is obs erv ed3 to fall wit h has
1 Giv en 17. A thin sem i-ci rcu lar ring of radius r
term ina l velocity 2 x 10- ms - . a pos itiv e cha rge q distributed uniform.ly
g = 9.8 m s- , viscosity of the air = 1.8 x
2 ➔
.
ove r 1t. The net field E at the centre O 1s
10-5 Ns m - and the den sity of oil =
2
[CTQ]
900 kg m- , the mag nitu de of q is:
3
A

19 j
19
(a) 1.6 x 10- C (b) 3.2 x 10- C
19
19
(c) 4.8 x 10- C (d) 8.0 x 10- C
➔

14. Consider an electric field E = E;

where
E 0 is a con stan t. The flux thro ugh the --. L- - "j
._ ___L_ _ _...J :.--
shaded are a (as sho wn in the figure) due 0
to this field is . [CT Q]
z q ~
(b) -
(a) 41t2 € ,2 J
0

q ~

(c) - 21t2 € ,2 J
o • ended in a
18. A cha rge d oil dro p 18 :us p that it
uni for m field of 3 x 10 V/m so the
0
neit her falls nor rises. The charge ~
dro p wil l be (Take the mass of te c
= 9.9 x 10-15 kg andg== 10 mis10-l ' 8C
(a) 1.6 x 10-18 C (b) 3.2 x 10-1• C
8
(d) 4· x
(c) 3.3 x 10-18 C
_,41
·~ 01
barges+ 8q and-2q
· ~_ --p--ninnttcchat . are located
· 19• rwo andx == L respectively. The location
O
.

at.x== 01. ton the x-axis at which the net

(a)~ (b)$
of a ~ ; Id due to these two point charges
electric e
is zero is
(c)~ (d)~
L (b) 2L
(a) 4
(d) SL 23. A body of mass M and charge q is
(c) 4L o connected to a spring of spring constant
. . ed plane making an angle of 30
An inc1in . .fi k. It is oscillating along x-direction
zo. . th horizontal is placed m a um orm
about its equilibrium position, taken
wit~ ~al electric field 200 N/C as shown
bonzon f lk · to be at x = 0, with an amplitude A.
. the figure below. A body o ~ass g An electric field E is applied along the
ind h rge 5 mC is allowed to shde down x-direction. Which of the following
anca ffi'
{roro rest at a height of Im. _ I fthe coe c1ent statements incorrect? [CTQ]
of fri.Clt'on is o.2, find the time taken by the 2 (a) The new equilibrium position is at a
d to reach the bottom. [g = 9.8 mis ,
boy ~ . qE
1 v3 distance k from x = 0.
2
sin 300 = 2;cos 300 = 2 ]
(b) The total energy of the system is
2 2
► .!..mcilA2 +.!.. q E
£==200N/C 2 2 k
(c) The total energy of the system is
2 2
30° .!..mcilA2 _.!_ q E
2 2 k
(a) 0.92 s (b) 0.46 s
(d) The new equilibrium position is at a
(c) 23 s [CTQ]
(d) 1.3 s
distance 2qE from x = 0.
21• A thin spherical shell of radius R has k
charge Q spread uniformly over its 24. An electric dipole has a fixed dipole
surface. Which of the following graphs p,
moment which makes angle 0 with
most closely represents the electric field respect in x-axis. When subjected to an
E(r) produced by the shell in the range ➔ " . .
0~ r < oo, where r is the distance from the electric field E = Ei, 1t experiences a
➔ "
centre of the shell? torque t 1 =ti.When subjected to another
➔ ~ •
E(r) E(r)
electric field E 2 = v3 E1J , it experiences
(a) I I\ }b) j\_ , t 1• The angle e.1s:-
t2 = ➔
torque ➔

at-+= ~
E(r) E(r)
(a) 60°
(c) 30°
(b) 90°
(d) 45°
25. Charges -q and +q located at A and B,
(c)~,(d) ~ , respectively, constitute an electric dipole.
Distance AB = 2a, 0 is the mid-point of
the dipole and OP is perpendicular to AB.
22. A long cylindrical shell carries positive A charge Q is placed at P where OP= y
surface charge 'cr' in the upper half and andy >> 2a. The charge Q experiences an
negative surface charge '-cr' in the lower electrostatic force F. If Q is now moved
halt: The electric field lines around the
cylinder will look like figure given in : along the equatorial line to P' = ( ~) such
(figures are schematic and not drawn to that, the force on Q will be close to:
scale)
 !P 3
X
''
''
'
(a) -½
' x2
Q+P'
:o
A•:=q·····r····+q" B (d) 5-
xl
29. Two particles A and B h .
F
(a) 3 F (b) 3 20 C d av1ng ch
µ ~n -5 µC respective} arges
fixed with a separation of 5 Y are held
(c) 9 F (d) 27 F .
position a third charged parti~:~ At What
26. A particle of mass m an~ charge q ~s placed so that it does not exp . houJdbe
released from rest in a umform elect~c electric force? erience anet
field. If there is no other force on t e
particle the dependence of its speed v on
20µC
~•---;-- _____-Sµc
5cm B
A
the dist~nce x travelled by it is correctly
given by (graphs are schematic a~Tnot (a) At 5 cm from 20 µC on the left .
system side of
drawn to scale) [ Q]

(a)il:=- (b)k, (b) At 5 cm from-5 µCon the right side

(c) At 1.25 cm from - 5 µC between two
charges

(c)~ (a)u (d) At mid-point between two charges

30. An electron with kinetic energy K enters
between parallel plates of a capacitor at
an angle 'a' with the plates. It leaves the
plates at angle 'B' with kinetic energy K.
1

27• Two charged thin infinite plane sheets of

uniform surface charge density cr+ and cr_, Then the ratio of kinetic energies K : ~
1
where lcr+I > lcr_l, intersect at right angle. will be : [CTQ]
2
Which of the following best represents the sin ~ 2
(a) - 2 - (b) co\~
electric field lines for this system? [CTQ] cos a cos (l

(b) .cr,O'_
cos~
(c) ~
cos~
(d) ~

31. In a regular polygon of n sides, each co~er

is at a distance r from the centre. Identical
charges of magnitude Q are placed_at
(n - 1) corners. The field at the centre is
[CTQI
Q nQ
(a) 4ne r 2 (b) 41tE/
28. Charges Q1 and Q2 are at points A and B 0
of a right angle triangle OAB (see figure (n - l)Q
(n-2)Q
(d) ~ ·
1
below). The resultant electric field at point 41ter
\:c) ----;;-
4ne nr2 0

0 is perpendicular to the hypotenuse, then o Q re placed at the

Qi'Q2 is proportional to [CTQ] 32. Four charges equal to - ad barge qis
A four corners o a squa . . ac uilibriUIIl
f rean
QI . centre. If the systern ism eq
at its
the value of q is
(a) - Q (1 + 2✓2) (b) ~ (1 +2./2)
2
2
(c) _g(t + 2Ji.)
4
 OH Qu1stlOHB ➔ ➔. 1t
p and E ts - and taking th'18 .
2 onentation
Reasoning (R)
as the refer level.
and Ris the correct
. . (A): When an electr'~ d';oe~
7. Assertion 1
•
true but R is not the placed m a non-uniform electric field .
·onof A. general, it experiences a force as weli :
torque.
Reason (R): The forces acting on the two
charges of dipole are unequal and their line
tion (A): If a proton and an electron of action is different.
1, Asse;aced in the same uniform electric field
areP 'fli . IPt1tt1(ftt1pA 8t1sod Q1409tl0Hs
they experience d1 erent acce1eratlons.
Reason (R): Electric force on a charge is I. A system of two equal and opposite charges
independent of its mass. (± q) separated by a small distance is called
Assertion (A): A copper ball is suspended an electric dipole. Electric dipole moment
2· with a non-conducting thread in a uniform is product of magnitude of charge and the
horizontal electric field. It is irradiated distance between the charges. It is a vector
with highly energetic y-radiations. The quantity directed from negative charge to
ball moves in the direction of electric field. positive charge. Its SI unit is C-m.
Reason (R): On irradiation, electrons are Read the above paragraph and answer the
ejected from the ball and the ball acquries questions that follow:
a net positive charge.
Equatorial plane
3. Assertion (A): When an electric dipole is
placed in a non-uniform electric field, only
rotational motion ofthe dipole is observed.
There is no translational motion.
Reason (R): The net force and the net
torque on the dipole are both non-zero. Axial
a➔ line
4. Assertion (A): Electric field intensity at
a point depends on the charge kept at that "''"--r---
point.
(i) A point that lies on the axial line is
Reason (R): Electric field intensity obeys
(a) P (b) Q
superposition principle.
(c) R (a) s
S. Assertion (A): When an electric dipole is
placed in a uniform electric field such that (ii) A point that lies on the equatorial line is
(a) P (b) Q
angle between pand Eis 90°, the dipole
(c) R (a) S
is in equilibrium.
(iii) The formula for dipole moment is
Reason (R): At equilibrium net force and ➔ ➔
(a) q x a (b) q x 2a
net torque both should be zero. ➔ ➔
(c) p x a (a) p x 2a
6. Assertion (A): The potential energy of a
OR
dipole in a uniform electric field is given
➔ ➔ The electric field intensity at point P for
bYthe expression U = - p . E . a short dipole is
➔ ➔
Reason (R): This formula comes into ➔ 1 p ➔ 1 p
(a) E = - - (b) E = - -
picture when we assume the potential 41tEo r3 41tEo a3
energy to be zero when the angle between .... 1 2p
➔

(c) E = 1t£
4
7 (a) None of these
0
 (iv) The ratio of electric field intensity at P
and Q for a short dipole is
➔
Er = 1
i i
(b:-.I ➔,, = --4
(a) ~
Eo
4 Eo

!,,
➔

(c) = 2 (d) :,, = - 2

E0 Ea .
Il When an electric dipole is placed in an el~ctrc1~
. f 1
field, then charges O d'pole expenen
be equal
forces. The magni~de offorces m:~f
or unequal depend~g on the ~ under the
electric
• The field lines originate f
charge and terminate at th rorn Po .
s1tive
field. Further the dipole may e the dipole charge. e negative
influence of a torque. Furthermore d hich • The direction of electric field st
will have some potential energy store . wfi Id
depends on its orientation in the electric e . point is given by the tangent dr;ength at a
Read the above paragraph and answer the °
electric field line at that point. wn 0 the
questions that follow: . . • The field lines are continuous.
(i) What is the net force on an ~lectn~dipole • The field lines never intersect.
placed in a uniform electnc field.
• In a region of the strong electric field .
(a) pE sin 8 1
(b) pE cos 8
are _very c1ose to each _other whereas ,inllles
the
(c)-pE cos 8 (d) zero . region of weak electric field lines are f:
(ii) What is the magnitude of torqu~ actmg ar.
on the dipole in a uniform electric field? • In the region of uniform electric field lin
there are equidistant parallel lines havine,
(a) pE sin 8 (b) pE cos e . .
the same dtrectlon. g
(c)-pE cos 0 (d) zero
The field lines are always normal to the
(iii) What is the potential energy of the dipole
surface of the conductor.
placed in a uniform electric field?
(a) pE sin 8 (b) pE cos 0
Read the above paragraph and answer the
questions that follow:
(c)-pE cos 8 (d) zero
(i) A few electric field lines for a system
OR
➔ ➔
of two charges QI and Q2 fixed at two
What is the angle between p and E for different points on the x-axis are shown
stable equilibrium? in the figure below. These lines suggest
(a) 180° (b) 0° that
(c) 90° (d) 45°
(iv) What is the potential energy change
when the dipole is rotated from unstable
equilibrium to stable equilibrium?
(a) 2pE (b) -2pE
(c) pE (d) -pE

Tllo concept of electric field lines was

Jim:oduced by Michael Faraday. It is used to
the nature of electric field in a given (a) IQ1I> IQ2I
.G properties of electric field lines (b) IQ1I < IQ2I . e left of Q1 the
are (c) at a finite distance to th
electric field is zero
(d) None
 .. Refer the above question and choose the (iv) A point positive charge is brought near
(u) correct statement an isolated conducting sphere (see figure
(a) IQ11= IQ2I
below). The electric field is best given by
(b) Qt is negative and Q2 is positive
(c) The electric field will b~ ze~~ s~me where
at a point lying on the hne Jommg QI and
Q2 between Q1 and Q2
(d) At a finite distance to the right of Q21 the
electric field will be zero. (a)

("i) A metallic solid sphere is placed in a

u uniform electric field. The line of force
follow the path shown in figure below as

1 I
(b)
2 2
3 3
4 4

(a) 1 (b) 2
(c) 3 (d) 4
OR (c)

A metallic shell has a point charge 'q'

kept inside its cavity. Which one of the
following diagrams correctly represents
the electric lines of forces?

(a) (d)
(a) Fig. (a) (b) Fig. (c)
(c) Fig. (b) (d) Fig. (d)
OR
(c) ....14--k' Electric field lines are
(a) continuous (b) form closed loops
(c) are discontinuous
(d) are always curved