(c) charge 2q between charges q and 8q and 5 cm from the charge q.
(d) charge 2q between charges q and 8q and 7 cm from the charge q.
8. Which of the following statements is incorrect regarding equipotential surfaces?
(a) Equipotential surfaces are closer in regions of large electric fields compared to regions of lower electric fields.
(b) Equipotential surfaces will be more crowded near sharp edges of a conductor.
(c) Equipotential surfaces will be more crowded near regions of large charge densities.
(d) Equipotential surfaces will always be equally spaced.
9. An electric dipole of length 2 cm is placed with its axis making an angle of 30° to a uniform electric field 105 N C–1. If it experiences a torque of 10 3 N m, then the potential energy of the dipole is (a) – 10 J (b) – 20 J (c) – 30 J (d) – 40 J 10. The arrangement consists
P Q of four identical plates.
Each plate has the area A and the plate separation is d. The equivalent capacitance between P and Q is potential at a point distant r (r > a) in a direction making an angle q from y-axis will be
(a) kq such that the surface charge densities on both the spheres are equal. The potential at their common centre is
Assertion & Reason Type
Directions : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as :
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If both assertion and reason are false.
13. Assertion : When two conductors charged to different potentials are connected to each other, the negative charge always flows from lower potential to higher potential.
Reason : In the process of charging there is always a flow of electrons only.
14. Assertion : The potential difference between two concentric spherical shells depends only on the charge of inner shell.
Reason : The electric field in the region in between two shells depends on the charge of inner shell and electric field is the negative of potential gradient.
15. Assertion : If the distance between parallel pates of a capacitor is halved and dielectric constant is made three times, then the capacitance becomes six times.
Reason : Capacitance of the capacitor does not depend upon the nature of the material of the plates.
JEE MAIN / JEE AdvANcEd / PETs Only One Option Correct Type
16. A capacitor is made of two circular plates of radius R each, separated by a distance d<<R.
The capacitor is connected to a constant voltage. A thin conducting disc of radius r << R and thickness t << r is placed at a centre of the bottom plate. What is the minimum voltage required to lift the disc if the mass of the disc is m?
17. Two conducting spheres, one of radius 5.88 cm and the other of radius 12.2 cm, each have a charge of 28.6 nC and are very far apart. If the spheres are
subsequently connected by a conducting wire, then the potential of each sphere, will be
(a) 2350 V (b) 2850 V (c) 1530 V (d) 1810 V
18. A total amount of positive charge Q is spread onto a non-conducting, flat, circular annulus of inner radius a and outer radius b. The charge is distributed so that the charge density (charge per unit area) is given by s = k/r3, where r is the distance from the centre of the annulus to any point on it and k is a constant. The potential at the centre of the annulus will be the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q when it is displaced by a small distance x along the x-axis is approximately proportional to
(a) x (b) x2 (b) x3 (d) 1 x More than One Options Correct Type
20. A parallel plate capacitor is formed by two identical plates, each of area A, separated by a small distance d. One plate has a total charge Q and the other Q′.
Neglect the edge effects then
(a) The charge per unit area on the outside of each plate is (Q + Q′)/ 2A.
(b) The charge per unit area on the outside of each plate is (Q – Q′)/2A.
(c) The potential energy of the dipole is 0.6 J.
(d) If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3 J.
22. Six point charges are kept at the vertices of a regular hexagon of side L and centre O as shown in figure
Given that K q V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and the work done on the system, in question, in the process of inserting the slab, then
(a) Q AV
24. A soap bubble 10 cm in radius with a wall thickness of 3.3 × 10–6 cm is charged to a potential of 70 V.
The bubble bursts and falls as a spherical drop. The potential of the drop (in kV) is
25. When a series combination of two uncharged capacitors is connected to a 12 V battery, 173 mJ of energy is drawn from the battery. If one of the capacitors has a capacitance of 4 mF, the capacitance of the other capacitor (in mF) is
26. A point charge of 2 mC moves from point P to point S along the path PQRS in a uniform electric field of 3 × 106 N C–1, as shown in the figure.
The co-ordinates of points P, Q, R and S are (0, 0, 0), (1, –1, 0), (2, 0, 0) and (1, 1, 0) respectively. The work done (in J) by the electric field in the process is
y radius a is surrounded by a thin uncharged concentric conducting shell of radius 2a. A point charge q is placed at a distance 4a from
common centre of conducting sphere and shell. The inner sphere is then grounded.
27. The charge on solid sphere is (a) −q
2 (b) −q
4 (c) − q
8 (d) − q 16 28. The potential of outer shell is
(a) q
29. Column I gives the dependence of electric potential (V) on distance (r) due to certain charged objects and Column II lists these objects. Match the entries of Column I with the entries of Column II.
Column I Column II (A) r–2 (P) Electric monopole (B) r–1 (Q) Electric dipole
(on the axial line) (C) r0 (R) Electric dipole
(on the equatorial line) (D) r–3 (S) Electric quadruple
(on the axial line)
(T) Charged spherical conductor (for an inside point)
A B C D are placed at origin. A circle of radius R with centre at origin is drawn as shown in figure.
Match the statements in Column I with the corresponding coordinates in Column II.
Column I Column II
(A) T h e c o ord i n ate s point on circle where potential is zero.
point on circle where magnitude of electric field intensity is point on circle where magnitude of electric field intensity is
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single oPtion correct tyPe
1. Two blocks m1 and m2 are connected with a compressed spring and placed on a smooth horizontal surface as shown in figure.
Force constant of spring is k. Under the influence of forces F1 and F2. At an instant blocks move with common acceleration a0. At that instant force F2 is suddenly withdrawn. Mark correct option.
(a) Instantaneous acceleration of m1 is a1 = a F
0 m1
1
− .
(b) Instantaneous acceleration of m2 is
a a F
2 0 m2
2
= + .
(c) Instantaneous acceleration of m 1 is a1 = 0.
(d) Instantaneous acceleration of m2 is a2 = 0.
2. Consider a one-dimensional collision where a body of mass m1 originally moving in the positive x direction with speed v0 collides with a second body of mass m2 originally at rest. The collision could be completely inelastic, with the two bodies sticking together, completely elastic, or somewhere in between. After the collision, m1 moves with velocity
v1, while m2 moves with velocity v2. If m1> m2, then
(a) v0 < v1 < v2 (b) v2 < v1 < v0 (c) v0 v v2 0
2 < < (d) v0 v2 v0 2 < <2
3. A smooth tunnel is dug along the radius of the earth that ends at the centre. A ball is released from the surface of earth along the tunnel. If the coefficient of restitution is 0.2 between the surface and ball
P
hysics Musing was started in August 2013 issue of Physics For You with the suggestion of Shri Mahabir Singh. The aim of Physics Musing is to augment the chances of bright students preparing for JEE (Main and Advanced) / AIIMS / Other PMTs with additional study material.In every issue of Physics For You, 10 challenging problems are proposed in various topics of JEE (Main and Advanced) / various PMTs. The detailed solutions of these problems will be published in next issue of Physics For You.
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