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TECH IIT D) AUTHOR OF IRODOV SOL

QUIZ - 1 Time=1.30 hr ELECTRO 12th TOPPERS [PHYSICS]

1 A point charge 50C is located in the XY plane at the point of position vector r0  2 i  3j . What is the electric

field at the point of position vector r  8i  5j
(A) 1200V/m (B) 0.04V/m (C) 900V/m (D) 4500 V/m

2. A nonconducting ring of radius R has uniformly distributed positive charge Q. A small part of the ring, of length d,
is removed (d << R). The electric field at the centre of the ring will now be
(A) directed towards the gap, inversely proportional to R3.
(B) directed towards the gap, inversely proportional to R2.
(C) directed away from the gap, inversely proportional to R3.
(D) directed away from the gap, inversely proportional to R2.

3. Two equal negative charges are fixed at the points [0, a ] and [0, –a] on the y-axis. A positive charge Q is released
from rest at the points [2a, 0] on the x-axis . The charge Q will
(A) execute simple harmonic motion about the origin
(B) move to the origin and remain at rest
(C) move to infinity
(D) execute oscillatory but not simple harmonic motion.

4. A small particle of mass m and charge –q is placed at point P on the axis of

uniformly charged ring and released. If R >> x, the particle will undergo
oscillations along the axis of symmetry with an angular frequency that is
equal to
qQ qQx qQ qQx
(A) 4 0 mR 3 (B) 4 0 mR 4 (C) 4 mR 3 (D) 4 mR 4
0 0

5. A charged particle having some mass is resting in equilibrium at a height H above the centre of a uniformly charged
non-conducting horizontal ring of radius R. The force of gravity acts downwards. The equilibrium of the particle
will be stable
R R R
(A) for all values of H (B) only if H > (C) only if H < (D) only if H =
2 2 2

6. An infinite nonconducting sheet of charge has a surface charge density of 10–7 C/m2. The separation between two
equipotential surfaces near the sheet whose potential differ by 5V is
(A) 0.88 cm (B) 0.88 mm (C) 0.88 m (D) 5 × 10–7 m

7. Four equal charges +q are placed at four corners of a square with its centre at origin and lying in yz plane. The
electrostatic potential energy of a fifth charge +q’ varies on x-axis as:

(A) (B) (C) (D)

8. Two identical thin rings, each of radius R meter are coaxially placed at distance R meter apart. If
Q1 and Q2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a
charge q from the centre of one ring to that of the other is
(A) zero (B) qQ1Q 2  2 1/  2.4 0 R 
(C) q 2Q1Q2  / 40 R (D) qQ1Q 2  2 1/  2.4 0 R 

9. Two positively charged particles X and Y are initially far away from each other and at rest. X begins to move
towards Y with some initial velocity. The total momentum and energy of the system are p and E.
(A) If Y is fixed, both p and E are conserved. (B) If Y is fixed, E is conserved, but not p.
(C) If both are free to move, p is conserved but not E (D) If both are free, E is conserved, but not p.
10. Two particles X and Y, of equal mass and with unequal positive charges, are free to move and are initially far away
from each other. With Y at rest, X begins to move towards it with initial velocity u. After a long time, finally
(A) X will stop, Y will move with velocity u. (B) X and Y will both move with velocities u/2 each.
(C) X will stop, Y will move with velocity < u. (D) both will move with velocities < u/2.

11. In space of horizontal EF (E = (mg)/q) exist as shown in figure and a mass m

attached at the end of a light rod. If mass m is released from the position shown in
figure find the angular velocity of the rod when it passes through the bottom most
position

g 2g 3g 5g
(A) (B) (C) (D)
l l l l

12. Two identical particles of mass m carry a charge Q each. Initially one is at rest on a smooth horizontal plane and the
other is projected along the plane directly towards first particle from a large distance with speed . The closed
distance of approach be
1 Q2 1 4Q 2 1 2Q 2 1 3Q 2
(A) (B) (C) (D)
4 0 m 4 0 m 2 4 0 m 2 4 0 m 2

13. The diagram shows a small bead of mass m carrying charge q. The bead can freely
move on the smooth fixed ring placed on a smooth horizontal plane. In the same
plane a charge +Q has also been fixed as shown. The potential atthe point P due to
+Q is V. The velocity with which the bead should projected from the point P so that
it can complete a circle should be greater than

6qV qV 3qV
(A) (B) (C) (D) none
m m m

14. A charged particle of charge Q is held fixed and another charged particle of mass m and charge q (of the same sign)
is released from a distance r. The impulse of the force exerted by the external agent on the fixed charge by the time
distance between Q and q becomes 2r is
Qq Qqm Qqm Qqm
(A) 4 0 mr (B) 4 0 r (C)  0 r (D) 2 0 r

15. Figure shows equi-potential surfaces for a two charges system. At which of the
labeled points point will an electron have the highest potential energy?
(A) Point A (B) Point B
(C) Point C (D) Point D


16. A uniform electric field having strength E is existing in x-y plane as shown in
figure. Find the p.d. between origin O & A(d, d, 0)
(A) Ed (cos + sin) (B) –Ed (sin – cos)

(C) 2 Ed (D) none of these

17. The diagram shows three infinitely long uniform line charges placed on the X,
Y and Z axis. The work done in moving a unit positive charge from (1, 1, 1) to
(0, 1, 1) is equal to
(A) ( ln 2) / 20 (B) ( ln 2) /0
(C) (3 ln 2) / 20 (D) None
18. A wheel having mass m has charges +q and –q on diametrically opposite points. It
remains in equilibrium on a rough inclined plane in the presence of uniform vertical
electric field E =

mg mg mg tan 
(A) (B) (C) (D) none
q 2q 2q

19. An equilateral triangle wire frame of side L having 3 point charges at its vertices is
kept in x-y plane as shown. Component of electric field due to the configuration in
z direction at (0, 0, L) is [origin is centroid of triangle]
9 3 kq 9 kq
(A) (B) zero (C) 8 L2 (D) None
8 L2

20. A, B, C, D, P and Q are points in a uniform electric field. The potentials a these
points are V (A) = 2 volt. V (P) = V (B) = V (D) = 5 volt. V (C) = 8 volt.
The electric field at P is
(A) 10 Vm–1 along PQ (B) 15 2 V m–1 along PA
A
(C) 5 V m–1 along PC (D) 5 V m–1 along PA

21. A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far
 
away from the dipole and at equal distance from it. The field at A and B are E A and E B .
   
(A) E A  E B (B) E A  2E B
  1  
(C) E A  2E B (D) | E B |  | E A | , and E B is perpendicular to E A
2

22. The dipole moment of a system of charge +q distributed uniformly on an arc of radius R subtending an angle /2 at
its centre where another charge -q is placed is :
2 2qR 2qR qR 2qR
(A) (B) (C) (D)
   

23. A large sheet carries uniform surface charge density . A rod of length 2l has a
linear charge density  on one half and – on the second half. The rod is hinged at
mid point O and makes an angle  with the normal to the sheet. The torque
experienced by the rod is
l 2
(A) 0 (B) 2 sin
0

l 2 l
(C)  sin (D) 2
0 0


24. Electric flux through a surface of area 100 m2 lying in the xy plane is (in V-m) if E  î  2ˆj  3k̂
(A) 100 (B) 141.4 (C) 173.2 (D) 200

25. An infinite, uniformly charged sheet with surface charge density  cuts through a
spherical Gaussian surface of radius R at a distance x from its center, as shown in
the figure. The electric flux  through the Gaussian surface is

(A)
R 2
(B)
 
2 R 2  x 2 
(C)
R  x 2 
(D)
 
 R2  x2 
0 0 0 0
26. Two spherical, nonconducting, and very thin shells of uniformly distributed positive
charge Q and radius d are located a distance 10d from each other. A positive point
charge q is placed inside one of the shells at a distance d/2 from the center, on the
line connecting the centers of the two shells, as shown in the figure. What is the net
force on the charge q?
qQ qQ 362qQ 360qQ
(A) 361 d 2 to the left (B) 361 d 2 to the right (C) 361 d 2 to the left (D) 361 d 2 to the right
0 0 0 0

27 Three large parallel plates have uniform surface charge densities as shown in the
figure. What is the electric field at P.

4 4 2 2
(A) – k̂ (B)  k̂ (C) – k̂ (D) k̂
0 0 0 0

 a  a
28. Positive and negative point charges of equal magnitude are kept at  0,0,  and  0,0,–  , respectively. The work
 2  2
done by the electric field when another positive point charge is moved from (–a, 0, 0) to (0, a, 0) is
(A) positive (B) negative
(C) zero (D) depends on the path connecting the initial and final positions

q q 2q y
29. Consider a system of three charges , and – placed at points A, B and C,
3 3 3 B
respectively, as shown in the figure. Take O to be the centre of the circle of radius
R and angle CAB = 60° C x
O
Figure : 60°

A
q
(A) The electric field at point O is 8 R 2 directed along the negative x-axis
0
(B) The potential energy of the system is zero
q2
(C) The magnitude of the force between the charges at C and B is
540 R 2

q
(D) The potential at point O is 12 R
0

30. Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an elliptical orbit. 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