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LAKSHYA JEE AIR (2025)

Electrostatics DPP-09

1. A particle of charge –q and mass m moves in a 3. A particle of mass m and charge q is fastened to
circle of radius r around an infinitely long line one end of a string of length l. The other and of
charge of linear charge density + . Then time the string is fixed to the point O. The whole
period will be given as: system lies on a frictionless horizontal plane.
Initially, the mass is at rest at A. A uniform
electric field in the direction shown in then
switched on. Then :

m 42 m 3
(1) T = 2r (2) T2 = r (1) The speed of the particle when it reaches B
2Kq 2Kq
2qEl
1 2Kq 1 m is
(3) T = (4) T = m
2r m 2r 2Kq
(2) The speed of the particle it reaches B is
qEl
2. Electric charge is uniformly distributed along a
m
long straight wire of radius 1mm. The charge per
cm length of the wires is Q coulomb. Another (3) The tension in the string when the particle
cylindrical surface of radius 50 cm and length 1m reaches at B is qE
symmetrically encloses the wire as shown in the (4) The tension in the string when the particle
The total electric flux passing through the reaches at B is zero
cylindrical surface is:
4. The electric field in region is given by
E = 200i N/C for x > 0 and −200i N/C for x < 0.
A closed cylinder of length 2m and cross -section
area 102m2 is kept in such a way that the axis of
cylinder is along X-axis and its centre coincides
with origin. The total charge inside the cylinder
is given as. Take the value of
Q 100Q
(1) (2) 0 = 8.85 10−12 C2m2 N:
0 0
(1) Zero
10Q 100Q
(3) (4) (2) 1.86 × 10–5C
(0 ) (0 )
(3) 1.77 ×10–11C
(4) 35.4 ×10–8C
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5. Consider the shown uniform solid insulating 8. Two spherical conductors B and C having equal
sphere of mass m with a short and light electric radii and carrying equal charges repel each other
dipole moment PJ embedded at its centre placed with a force F when kept apart at some distance.
at rest on a horizontal surface An electric field A third spherical conductor having same radius
as that of B but uncharged is brought in contact
Ei is suddenly switches on in the region such with B, then brought in contact with C and finally
that the sphere starts rolling without sliding. removed away from both. The new force of
Speed of the sphere when the dipole becomes repulsion between B and C is:
horizontal for the first time is given as (1) F/4
(2) 3F/4
(3) F/8
(4) 3F/8

9. Figure shown a section through two long thin

concentric cylinders of radii a & b with a > b. The
5pE 10pE cylinders have equal and opposite charges per
(1) (2)
m 7m unit length . Find the electric field at a distance
5pE r from the axis for (a) r <a, (b) a < r < b, (iii) r >b
(3) (4) Zero
2m
6. A loop of diameter d is rotated in a uniform
electric field until the position of maximum
electric flux is found. The flux in this position is
measured to be . What is the electric field
strength?
4 2
(1) (2)
d 2
d 2
 d2
(3) (4)
d 2 4
7. A semi-infinite insulating rod has linear charge 10. A point charge Q is located on the axis of a disc
density . The electric field at the point P shown of radius R at a distance a from the plane of the
in this figure disc. If one fourth of the flux from the charge
passes through the disc, then find the relation
between a & R:

11. A very long uniformly charged thread oriented

along the axis of a circle of radius R rests on its
centre with one of the ends. The charge of the
thread per unit length is equal to . Find the flux
2 2
(1) at 45º with AB
( 40 r )2 of the vector E across the circle area:

2 2
(2) at 45º with AB
40 r 2
2
(3) at 45º with AB
40 r
2
(4) at 135º with AB
40 r
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Answer Key
1. (1)  2K 
2. (2)
9. 0, r ,0
3. (2)
 R
4. (4) 10. a = 
 3
5. (2)
1
6. (1) 11. [ = R / 0 The sign of  depends on how the
7. (3) 2
8. (4) direction of the normal to the circle is chosen.]

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