Question

Two conducting spheres of different sizes are at the same potential. The radius of the larger sphere is four times larger than that of the smaller sphere. If a total charge Q is placed on this system, what fraction of Q sits on the larger sphere?(Give your answer as a decimal. For example, if the answer is 1/3 then input 0.333.)

Answer 1

Answer:

0.8

Explanation:

The two spheres have the same potential, V.

Let the radius of the larger sphere be R and the radius of the smaller sphere be r,

=> R = 4r

Let the charge on the smaller sphere be q. Hence, the larger sphere will have charge Q - q.

The potential of the smaller sphere will be:

$V_S = \frac{kq}{r}$

The potential of the larger sphere will be:

$V_L = \frac{k(Q - q)}{R}$

Inputting R = 4r,

$V_L = \frac{k(Q - q)}{4r}$

Since $V_S = V_L = V$,

$\frac{k(Q - q)}{4r} = \frac{kq}{r}$

=> Q - q = 4q

=> 5q = Q

q = 0.2Q

The fraction of the charge Q that rests on the smaller sphere is 0.2

The charge of the larger sphere is:

Q - q = Q - 0.2Q = 0.8Q

∴ The fraction of the total charge Q that rests on the larger sphere is 0.8