Question

A small charged ball lies within the hollow of a metallic spherical shell of radius R. For three situations, the net charges on the ball and shell, respectively, are (1) +4q, 0; (2) –6q, +10q; (3) +16q, –12q. Rank the situations according to their charge on (a) the inner surface of the shell and (b) the outer surface, most positive first

Answer 1

Situation (1) has the most positive charge on the inner surface of the shell, while situation (2) has the most positive charge on the outer surface.

Step-by-step explanation:

To rank the situations according to their charge on the inner and outer surfaces of the metallic spherical shell, we need to consider the net charges on the small charged ball and the shell. Let's analyze each situation:

1. For situation (1) with a net charge of +4q on the ball and 0 charge on the shell: (a) The inner surface of the shell has a charge of +4q, and (b) the outer surface has a charge of 0.
2. For situation (2) with a net charge of -6q on the ball and +10q on the shell: (a) The inner surface of the shell has a charge of -6q, and (b) the outer surface has a charge of +10q.
3. For situation (3) with a net charge of +16q on the ball and -12q on the shell: (a) The inner surface of the shell has a charge of +16q, and (b) the outer surface has a charge of -12q.

Therefore, ranking the situations according to the charge on the inner surface would be: (1), (3), (2) - from most positive to least positive. For the outer surface, the ranking would be: (2), (1), (3) - from most positive to least positive.

Answer 2

Part a)

2) > 1) > 3)

Part b)

1) = 2) = 3)

Step-by-step explanation:

Due to charge induction the magnitude of charge on the inner surface of the outer shell is having same charge as that of the small sphere inside but the sign of charge must be opposite.

So here we can say

1)+ 4q, 0

so inner surface has charge - 4q and outer surface charge is +4q

2) -6q , +10q

so inner surface charge is +6q, outer surface charge is +4q

3) +16q , -12q

so inner surface charge is -16q, outer surface charge is +4q

Part a)

situations in which inner surface charge is arranged in decreasing order is given as

2) > 1) > 3)

Part b)

Situations in which outer surface charge is arranged in decreasing order is given as

1) = 2) = 3)