Yashpatil TG~ @bohring_bot ELECTROSTATICS
1. Which type of electrostatic field E is not possible ?
(A) E yiˆ (B) E xjˆ (C) E yiˆ xjˆ
(D) x 2 3yiˆ xjˆ
2. A capacitance C is connected between every two vertices of a cube (including the body diagonals and the face
diagonals). The effective capacitance of the system across any edge is :
(A) C (B) 3C (C) 2C (D) 4C
e
a br
3. A charge distribution generates a radial electric field E e where a and b are constant. The total charge
r2
giving rise electric fields is
(A) 4 0a (B) 4 0 b (C) 4 0ab (D) 0
4. A dipole is placed at origin of co-ordinates system as shown in figure. Electric field at
point P(0, y) is given as
k k ˆ
(A)
3y3
ˆi ˆj (B)
y3
i 2ˆj
k ˆ ˆ k
(C)
y3
i 2 j (D)
2y 3
ˆi 2ˆj
5. Two concentric conducting spheres of radii R and 3R carrying charges Q and 2Q respectively. If the charge on
inner sphere is doubled. The potential difference between inner and outer spheres will
(A) becomes two times (B) becomes four times (C) be halved (D) remains same
6. Two fixed charge –2Q and Q are located at the point of co-ordinates (–3a, 0) and (3a, 0) respectively in (x – y)
plane. Then all the points in x – y plane where potential is zero lies on a
(A) Straight line parallel to x-axis (B) straight line parallel to y-axis
(C) a circle of radius 4a (D) Circle of radius 2a
7. In the adjacent figure the switch S is closed t = 0, QA, QB and QC are charge on the
capacitor A, Capacitor C in the steady state respectively. Choose the correct
statement.
(A) QA QB QC (B) QA QC QB
(C) QC QA QB (D) QC QB QA
8. Two points A and B are at distances of ‘a’ and ‘b’ respectively from an infinite conducting plate charge density
. The work done in moving charge Q from A to B is
Q Q
(A) b a (B) Q (C) (D) None of these
0 b a b a 0
9. The diagram shows four pairs of large parallel conducting plates. The plates are separated by equal distance in
all cases. The value of the electric potential is given for each plat. Rank the pairs according to the magnitude of
the electric field between the plates. Least to greatest.
(A) 1, 2, 3, 4 (B) 4, 3, 2, 1 (C) 2, 3, 1, 4 (D) 2, 4, 1, 3
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 1
10.
Yashpatil TG~ @bohring_bot
Electrostatics
A conducting shell having inner radius R1 and ou8ter radius R2 contains a
charge +q which is placed at a distance x from its centre. Field at an exterior
point P which is situated at a distance r from centre of shell ( r > R2 )
(A) depends on x (B) depends on R1 and R2
(C) depends only or r (D) None
11. Two plates each of one side area ‘A’ are kept at a separation ‘d’. They have
charge Q1 and Q2 and uniform electric field E exist in the region as shown. Then
Q1 Q2 Q1 Q 2
(A) Charge on surface (1) is A 0 E (B) Field inside the gap E
2 2A 0
(C) Field outside the gap is E (D) Field on either side of the plates is identical
12. Figure shows a large conducting sheet having charge on both sheet. The
surface potential of sheet is V0. A sphere of radius r is placed at a distance
r from the sheet. When the key is closed charge q appears on the
surface. The values on sheet is given by
q 4 0 rV0 4 0 rV0 q
(A) (B)
4 r 2 r
4 0 rV0 q
(C) (D) Zero
2 r
13. Two rods each of length 6L carry charge Q are placed as shown in figure.
Find the magnitude of electric field at point P, which is at a distance of 5L
from centre of each rod.
1 3Q 5Q
(A) . 2 (B)
64 0 L 4 0 L2
1 Q 3Q
(C) . (D)
2 0 L2 5 0 L2
14. A solid sphere if radius R, and dielectric constant ‘k’ has spherical cavity radius R/4. A point charge q1 is placed
in the cavity. Another charge q2 is placed outside the sphere at a distance of r from q. Then Coulombic force of
intersection between them is found to be ‘F1’When the same charges are separated by same distance in
vacuum then the force of interaction between is found to be F2 then
1
(A) F1 F2 / k (B) F2 F1 / k (C) F1.F2 (D) F1 F2
k
15. A charged particle q is placed at a distance d from the centre of conducting sphere of radius R(<d), then in
static conditions at the centre of sphere
kq
(A) Magnitude of electric field due to induced charges is
d2
kq
(B) Magnitude of electric field due to induced charge is 2
R
(C) Magnitude of electric field due to induced charge is zero
kq
(D) Magnitude of electric field due to charge q is (where k = ¼ 0 )
d2
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 2
16.
Yashpatil TG~ @bohring_bot
Electrostatics
Suppose an electrostatics potential has a maximum at point A and a minimum at point B. Choose the correct
alternative:
(A) Point A is stable equilibrium point for both positive and negative charge
(B) Point B is stable equilibrium point for both positive and negative charge
(C) Point A is stable equilibrium point for positive and point B is stable equilibrium point for negative charge
(D) Point B is stable equilibrium point for positive and point A is stable equilibrium point for negative charge
17. Mark the INCORRECT statement
(A) By convention, the charge on a plastic rod rubbed with fur is negative and the charge on a glass rod rubbed
with silk is positive.
ke 2
(B) The ratio of electric force and gravitational force between a proton and electron is 2.4 1039
Gmemp
(C) Conservation of total charge of an isolated system is a property dependent on the scalar nature of charge.
(D) Quantisation of electric charge is a basic unexplained law of nature, interestingly; there is no analogues
law of quantisation of mass.
18. An infinite non conducting uniformly charged sheet has a hole of radius ‘R’ in it (change density = ). An
electron is placed on an axis passing through the centre of hole and perpendicular to the plane of sheet at a
distance ‘R’ from the centre. The speed with which the electron reaches the centre is
x
0 Given : electric field on the axis of a uniformly charged disc of radius ‘r’ E x 1 2 2
2 x r
(A)
eR
(B)
2 eR
(C)
2 1 eR (D)
2 eR
m 0 m 0 m 0 m 0
19. Rod of mass m and length carrying one charge in length x and negative charge remaining portion. Linear
charge density is same for both charges. Rod is hinged at end A.A uniform E perpendicular to rod is
switched on and rod remain in equilibrium. Find value of x. (consider gravity g is absent)
(A) x (B) x (C) x
2 2 2
3
(D) x
2
20. Consider a non-conducting ring of radius ‘a’ om x-y plane. The two semi-
circular portions have linear charge densities and as shown. Then :
(A) Dipole moment of the ring is 2 3iˆ 2ˆj a 2
(B) Dipole moment of the ring is 2iˆ 2 3jˆ a 2
(C) Electric field at the centre of the ring is
2 0 a
3iˆ ˆj
(D) Electric field at the centre of the ring is
2 0 a
ˆi 3jˆ
21. X and Y are large parallel conducting plates close to each other. Each face has an area A. X is
given a charge Q, Y us without any charge. Point A, B and C are shown.
Q Q
(A) Electric field at B is (B) Electric field at B is
2 0 A 0A
(C) The field at A, B and C ate same magnitude (D) The field at A and C are in opposite direction.
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 3
22.
Yashpatil TG~ @bohring_bot
Electrostatics
Electric field due to a ‘short’ electric dipole at a points P as shown in at an angle with respect to p . Then
tan
(A) tan 1
2
tan
(B) tan 1
2
tan
(C) tan 1
2 2
tan
(D) tan 1
5
23. A uniform vertical electric field E is established in the space between two large parallel plates. A small
conducting sphere of mass m is suspended in the field from a string of length L. If the sphere is given a positive
charge q and the lower plate is charged positively , the period of oscillation of this pendulum is
L L L L
(A) 2 (B) 2 (C) 2 (D) 2
g q qE / m q qE / m [g qE / m ]1/ 2
2 2
24. The equivalent capacitance of the circuit between A and B is
(A) 10 F
(B) 5 F
(C) 15 F
(D) 20 F
25. Three similar plates are arranged as shown in figure. If area of each plates is A and
a charge +Q is given plates then potential of middle plate is
3 Qd Qd
(A) (B)
4 A 0 4A 0
Qd Qd
(C) (D)
3A 0 2A 0
26. A parallel plate capacitor is dipped in an insulated, liquid, vertically so that
half of capacitor is in liquid. Plates of capacitor is in liquid. Plates of capacitor
are joined to an ideal battery of emf , A, B, A ', B' are four points on plate
at facing surface as shown. Which of the following is/are correct ?
(A) VA VB' VA VA'
(B) VB VB' VB VA'
(C) Electric field around A in air = Electric field around B’ in liquid.
(D) Electric field around N in liquid = Electric field around B’ in liquid.
27. A capacitor of capacitance ‘C’ is connected to a battery of emf as shown. After full charging
a dielectric of same size as that of capacitor & dielectric constant k is inserted. Then choose
the INCORRECT statement(s)
(capacitor remains always connected to battery)
(A) Electric field between plates of capacitor remains same
(B) Charge on capacitor increases to 2kC
(C) energy stored in capacitor decreases
(D) Electric field between plates of capacitor increases
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 4
28.
Yashpatil TG~ @bohring_bot
Electrostatics
Consider the circuits drawn below:
All the capacitor are identical, then
(A) CCD CEF CAB (B) CCD CEF CAB (C) CCD CAB CEF (D) CEF CCD CAB
29. Four conducting plates are arranged with equal spacing and surface of all
the plates are marked as 1, 2,3, 4, 5, 6, 7 and 8 as shown. Two middle plates
are given charged +Q and –Q, after which S1 and S2 are closed. The charge
distribution on the surface of conducting plates from 1 to 8 in order is :
(A) O, Q, Q, O, O, Q, Q, O
(B) O, Q / 3, Q / 3, 2Q / 3, 2Q / 3, Q / 3, O
(C) O, O, O, Q, Q, O, O, O
(D) O, 2Q / 3, 2Q / 3, Q / 3, Q / 3, 2Q / 3, 2Q / 3, O
30. There is a conductor with cavity of radius R as shown in figure. A point charge
Q is placed at R/2 distance from centre of cavity. A point P is at r distance from
centre of conductor. Then, which of the following is INCORRECT.
(A) Charge density at inner surface of cavity will be non-uniform
(B)Charge density at surface of conductor will be uniform
Q
(C) electric field at point P is
4 0 r 2
(D) force on charge Q is zero
31. In the given circuit diagram, find the heat generated on closing the switch S.
(initially the capacitor of capacitance C is unchanged)
3
(A) CV2 (B) CV 2
2
1
(C) CV2 (D) 2CV 2
2
32. A spherical conductor A of radius r is placed concentrically inside a conducting shell B of radius R(R>r). A
charge Q is given to A, and then A is joined to B by a metal wire. The charge flowing from A to B will be
R r
(A) Q (B) Q (C) Q (D) Zero
Rr Rr
33. A negative point charge is brought near an unchanged solid dielectric sphere.
Positive induced charges appear on the side of the sphere nearest to the point
charge, negative induced charges on the opposite side. A, B and C are three
points on diameter of the sphere that also passes through the point charge.
Comparing only at points A, B, and C on the dielectric sphere, the potential is
:
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 5
Yashpatil TG~ @bohring_bot
Electrostatics
(A) Largest at C (B) Largest at A (C) Largest at B (D) The same every where
34. A parallel plate capacitor with plate area A and separation d has charges Q. A slab of dielectric constant k is
inserted in space between the plates almost completely fills the space. If E0 , U0 and C0 be the electric field.
Potential; energy and capacitance before inserting the slab, then
E0
(A) The electric field after inserting the slab is
k
(B) The capacitance after inserting the slab is k C0
1
(C) The induced charged on the slab is Q 1
k
U
(D) The energy stored in the capacitor becomes 0 , U 0 being the energy of the capacitor before inserting
k
the slab
35. A point Charge is placed at a distance r from centre of a conducting neutral sphere of radius R(r>R). The
potential at any point P inside the P inside the sphere at a distance r1 from charge due to induced charge of
1
the sphere is given by [k = ]
4 0
(A) kq / r1 (B) kq / r (C) kq / r kq / r1 (D) kq / R 0
36. A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density .
The flux due to the charge q through the disc is . The electric force on charge q exerted by the disc is
(A) (B) (C) (D)
4 2 3
37. An uncharged conducting sphere of radius R, has a hollow cavity sphere of
R
radius , as shown. Which of the following is/are correct about
2 R
𝑅
electrostatic energy?
2
(A) Interaction energy of induced charge with charge placed at centre of Q
1 Q2
cavity is
4 0 R
(B) Interaction energy of induced charge with charge placed at centre of
1 Q2
cavity is
4 0 R
1 Q2
(C) Electrostatic energy outside sphere is
4 0 9R
1 Q2
(D)Electrostatic energy outside sphere is
4 0 R
38. A point-like body of mass m and of charge Q is initially at rest on the horizontal;
tabletop as shown in the figure and is given a v0 vertical, upwards speed. There is a
horizontal electric field E. Acceleration due to gravity = g
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 6
Yashpatil TG~ @bohring_bot
Electrostatics
v 02
(A) Maximum height attained
2g
2QEv 02
(B) Particle will collide with the table at horizontal distance
mg 2
(C) At the highest point acceleration will be only in horizontal direction.
mg
(D) Particle collide with the table at an angle tan with horizontal.
2QE
39. Electric field at point P in a region whose coordinates are (x, y, z) is given by : E E0
yiˆ xjˆ where E is
0
x 2 y2
constant . Which of the following can best represents the electric field line corresponding to this field?
(A) (B)
(C)
40. The diagram shows four system of charged particle. Each system contains two charged particle at points A and
point B as shown in figure. A third positive point charge q0 is kept at point P in each system. The direction of
electrostatic force experienced by the charge q0 will be
System –1 ; AP= BP=r and AB is a System –2; AP = BP = r and AB is a
straight line straight line
System –3 ; AP = BP = r and AB is a circular arc of System – 4 ; AP = BP = r and AB is a circular arc of
radius r and centre at O radius r and centre at O
System – 1 System –2 System –3 System – 4
(A)
(B)
(C)
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 7
Yashpatil TG~ @bohring_bot
Electrostatics
(D)
41. Terminal A is connected to positive terminal of battery and B is connected to negative terminal of plate and it
send same charge Q in all four combination. Each plate have same area are separation between two
consecutive plate is same.
Column – I Column – II
(A) (P) Top surface of plate 1 have zero charge
(B) (Q) Upper surface of plate 4 have –Q charge
(C) (R) Same charge Appear on both surface of plate 2
(S) Bottom surface of plate 4 have zero charge
(T) Total charge on plate 2 is Q
42. A semi circular disc of mass M and radius R with linear charge density
on its curved circumference is hinged at its centre and placed in a
uniform electric field as shown in the figure Match the statements from
List I with those in List II and select the correct answer using the code
below the lists.
Column – I Column – II
M
(A) The net force acting on the ring is (P)
E
If the ring is slightly rotated about O and
(B)
released. Find its time period of oscillation
(Q) R E
The work done by an external agency to 2K
(C) (R) E
rotate it through an angle is R
(D) Magnitude of electric field at ‘O’ will be (S) 4 ER 2 sin 2
2
43. A charge ‘q’ is undergoing S.H.M. about point ‘A’ along the line AB
at distance ‘d’ from the centre B of a conducting sphere of radius
R. Amplitude oscillation of charge is ‘a’ angular frequency is ' ' .
The sphere os grounded through conducing wire CC’ . Choose the
correct statement
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 8
Yashpatil TG~ @bohring_bot
Electrostatics
Ra
(A) if a d then the maximum value of current in wire CC’ will q 2
d
q Ra 2
(B) if a d then the maximum value of current in wire CC’ will be 3
d
2Ra
(C) if a d then the maximum value of current in wire CC’ will be q 2
d
2q Ra 2
(D) if a d then the maximum value of current in wire CC’ will 3
d
Paragraph Type
Ad
A parallel plate capacitor has plate area ‘A’ and plate separation ‘d’. A dielectric of volume and dielectric
2
constant ‘K’ is available. To use it in the capacitor, two alternative methods are available as shown:
0 A
44. Capacitance in case (1) is X1 . Then x1 is
d
K 2K 3k 1 2k
(A) (B) (C) (D)
3 k 1 2k K 1
0 A
45. Capacitance is case (20 is x 2 . Then x 2 is
d
K 1 K K 1 1 2K K K K 1
(A) (B) (C) (D)
4 K 1 4 K 4 3 3 2
46. Figure shows a irregular shape conductor with
irregular cavity inside it. A charge Q is placed inside
cavity and a charge Q’ is placed outside conductor. Let
'
Q ind be charge induced at outside surface of conductor
and Qind be the charge induced at inside surface of
cavity. A’ B’ is an arbitrary line passing through charge
Q and a, b, c, be the points on line as shown in figure.
' '
Let E, E ', E ind and Eind represents electric field at different points due to charge Q, Q’ Qind , & Q ind respectively.
If Va , Vb and Vc represents potential at point a, b, and c. choose the incorrect statement
(A) Va Vb Vc
rb
E E E Eind.dr, where rb positions vector of point b
' '
(B) Vb ind
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 9
Yashpatil TG~ @bohring_bot
Electrostatics
(C) Vb E ' E .dr
'
ind
(D) At point ‘b’, E ' 0
FIITJEE Durgapur MAIN Building A-3, Nandalal Bithi, 0343 254 2643, FIITJEE Durgapur, ANNEX Building C111 Kaji, Nazrul Sarani 0343 254 2642
FIITJEE National Office,29-A Near Hauz Khas Metro Station, Sarvapriya Vihar, Kalu Sarai, New Delhi, Delhi 110016 10
