Questions for iit jee electric charges and fields

Chapter 14

Electric Charges and Fields
1. A charge Q is placed at each of the opposite 4. Let there be a spherically symmetric charge
corners of a square. A charge q is placed at each distribution with charge density varying as
of the other two corners. If the net electrical force
5 r 
Q (r )  0  –  upto r = R, and r(r) = 0 for
on Q is zero, then equals [AIEEE-2009] 4 R
q
r > R, where r is the distance from the origin. The
(1) –1 electric field at a distance r(r < R) from the origin
(2) 1 is given by [AIEEE-2010]

1 0 r  5 r  40 r 5 r 
(3) – (1) 3  4 – R  (2)  – 
2 0   3 0 3 R

(4) –2 2 0 r  5 r  40 r 5 r 
(3) 4  3 – R  (4) 3 0
 – 
Q 0   4 R
2. Let (r )  r be the charge density distribution
R 4 5. Two identical charged spheres are suspended by
for a solid sphere of radius R and total charge Q. strings of equal lengths. The strings make an
For a point ‘p’ inside the sphere at distance r1 from angle of 30° with each other. When suspended in
the centre of the sphere, the magnitude of electric
a liquid of density 0.8 g cm–3, the angle remains
field is [AIEEE-2009]
the same. If density of the material of the sphere
is 1.6 g cm–3, the dielectric constant of the liquid
Q Q r12
(1) (2) is [AIEEE-2010]
40 r12 40 R 4
(1) 1 (2) 4
Q r12 (3) 3 (4) 2
(3) 4 (4) 0
30 R 6. Two positive charges of magnitude 'q ' are placed at
the ends of a side (side 1) of a square of side '2a'.
3. A thin semi-circular ring of radius r has a positive
Two negative charges of the same magnitude are
charge q distributed uniformly over it. The net field
 kept at the other corners. Starting from rest, if a
E at the centre O is [AIEEE-2010] charge Q moves from the middle of side 1 to the
centre of square, its kinetic energy at the centre of
^
j square is [AIEEE-2011]

1 2qQ  2 
(1) 1 
40 a  5
^
i
O
1 2qQ  1 
(2) 1  
q ˆj q 40 a  5
(1) (2) ˆj
2  0 r 2
2
4  0 r 2
2
(3) Zero
q q ˆj
(3) – jˆ (4) – 1 2qQ  1 
2 0 r 2
2 1
4  0 r 2 40 a  
2
(4)
5

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,7. In a uniformly charged sphere of total charge Q and
radius R, the electric field E is plotted as a
++ ++
function of distance from the centre. The graph (3) +
–– ––
+
which would correspond to the above will be : –– ––
[AIEEE-2012]

E E



(1) (2) (4)


R r R r
10. The region between two concentric spheres of radii
E E ‘a’ and ‘b’, respectively (see figure), has volume
A
charge density   , where A is a constant and
r
(3) (4) r is the distance from the centre. At the centre of
the spheres is a point charge Q. The value of A
R r R r such that the electric field in the region between
the spheres will be constant, is :
8. Two charges, each equal to q, are kept at x = – a [JEE (Main)-2016]
and x = a on the x-axis. A particle of mass m and
q
charge q0  is placed at the origin. If charge q0
2
is given a small displacement (y << a) along the a
Q
y-axis, the net force acting on the particle is
proportional to [JEE (Main)-2013] b
(1) y
(2) – y Q 2Q
(1) 2 2 (2)
2( b  a ) (a  b2 )
2
1
(3) 2Q Q
y
(3) 2 (4)
1 a 2a2
(4)  
y 11. An electric dipole has a fixed dipole moment p ,
9. A long cylindrical shell carries positive surface which makes angle q with respect to x-axis. When

charge s in the upper half and negative surface subjected to an electric field E 1  Ei , it
charge –s in the lower half. The electric field lines 
around the cylinder will look like figure given in experiences a torque T 1  k . When subjected to

[JEE (Main)-2015] another electric field E 2  3E1j it experiences a
 
(figures are schematic and not drawn to scale) torque T 2  T 1 . The angle q is
[JEE (Main)-2017]
(1) 30° (2) 45°
++++ (3) 60° (4) 90°
+ +
–– ––
(1) –– –– 12. Three charges +Q, q, +Q are placed respectively, at
distance, 0, d/2 and d from the origin, on the x-axis.
If the net force experienced by +Q, placed at x = 0,
is zero then value of q is [JEE (Main)-2019]

+
Q –Q
++
+ (1) (2)
––
++
–– 2 2
(2) –– ––
–Q Q
(3) (4)
4 4
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, 13. For a uniformly charged ring of radius R, the electric
y
field on its axis has the largest magnitude at a OP     , the force on Q will be close to
distance h from its centre. Then value of h is 3
y 
[JEE (Main)-2019]  3  2a  [JEE (Main)-2019]
 
R R P
(1) (2)
2 5
Q P
(3) R (4) R 2 A O
–q +q B

14. Two point charges q1  
10  C and q2(– 25 mC)
are placed on the x-axis at x = 1 m and x = 4 m
respectively. The electric field (in V/m) at a point
y = 3 m on y-axis is, [JEE (Main)-2019] F
(1) (2) 9F
3
 1 
 take  9  109 Nm2 C2  (3) 27F (4) 3F
 40  17. An electric field of 1000 V/m is applied to an
electric dipole at angle of 45°. The value of electric
(1)  63 iˆ  27 jˆ   10 2
dipole moment is 10–29 Cm. What is the potential
energy of the electric dipole? [JEE (Main)-2019]
(2)  81iˆ  81 jˆ   10 2 (1) –9 × 10–20 J (2) –10 × 10–29 J
(3) –7 × 10–27 J (4) –20 × 10–18 J
(3)   81iˆ  81 ˆj   10 2
18. Determine the electric dipole moment of the
system of three charges, placed on the vertices of
(4)   63 iˆ  27 ˆj   10 2 an equilateral triangle, as shown in the figure
[JEE (Main)-2019]
15. Charge is distributed within a sphere of radius R
2 r
A –2q
with volume charge density   r   2
e a , where y
r l l
A and a are constants. If Q is the total charge of +q
this charge distribution, the radius R is +q
l x
[JEE (Main)-2019] jˆ  iˆ
(1) 2ql ˆj (2) 3 ql
2
 
a  1  a  Q 
(1) log   (2) log  1   iˆ  jˆ
2  1  Q  2  2aA  (3)  3 ql jˆ (4)  ql 
 2aA  2
19. An electric dipole is formed by two equal and
  opposite charges q with separation d. The charges
 Q   1  have same mass m. It is kept in a uniform electric
(3) a log  1   (4) a log   field E. If it is slightly rotated from its equilibrium
 2aA   1  Q  orientation, then its angular frequency w is:
 2aA 
[JEE (Main)-2019]
16. Charges –q and +q located at A and B,
respectively, constitute an electric dipole. Distance 2qE qE
AB = 2a, O is the mid point of the dipole and OP (1) (2) 2
md md
is perpendicular to AB. A charge Q is placed at P
where OP = y and y >> 2a. The charge Q
experiences an electrostatic force F. If Q is now qE qE
(3) (4)
moved along the equatorial line to P¢ such that 2 md md

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