Charges on Conductors

Q.

If a hollow metal sphere is given a charge Q and another conducting sphere is placed inside it concentrically. A charge q is placed at the centre. The charge that appears on the surface B of the inner sphere is

1. +Q

2. +q

3. -q

4. zero

Q. A conducting spherical shell carrying a charge $Q$ has inner radius $a$ and outer radius $b$ . If a small electric dipole is placed at its center as shown in the figure then which of the following statements is true

1. Surface charge density on the inner surface of the shell is zero everywhere.
2. Surface change density on the inner surface is uniform and equal to $\frac{\left(Q/2\right)}{4\pi a^2}$
3. The electric field outside the shell is the same as that produced due to the point charge at the centre of the shell.
4. Surface charge density on the outer surface depends on $|\overrightarrow{p}|$

Q. Four metal conductors having different shapes
1. A sphere
2. Cylindrical
3. Pear
4. Lightning conductor

Which shape will sustain its charge for the longest time?

1. 1
2. 2
3. 3
4. 4

Q. A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself

1. Uniformly in the metal object
2. Uniformly on the surface of the object
3. Such that the potential energy of the system is minimised
4. Such that the total heat loss is minimised

Q. An isolated solid metallic sphere is given +Q charge. The charge will be distributed on the sphere

1. Uniformly but only on surface
2. Uniformly inside the volume

3. Only on surface but non-uniformly

4. Non-uniformly inside the volume

Q. There are two metallic spheres of same radii but one is solid and the other is hollow, then

1. Solid sphere can be given more charge
2. Hollow sphere can be given more charge
3. They can be charged equally (maximum)
4. None of the above

Q. In electrostatic condition, the net charge inside a conductor is always zero.

1. True
2. False

Q. The electric field inside a conductor is always zero.

1. True
2. False

Q. Conducting body is connected to Earth, a point charge (Q) is at distance r from point C, potential at point C is

1. $\frac{kQ}{r}$
2. zero
3. $\frac{KQ}{3r}$
4. $\frac{Kq}{2r}$

Q.

A positive charge q is placed in front of a conducting solid cube at a distance d from its centre. Find the electric field at the centre of the cube due to the charges appearing on its surface.