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:
[tex]V_S = \frac{kq}{r}[/tex]
The potential of the larger sphere will be:
[tex]V_L = \frac{k(Q - q)}{R}[/tex]
Inputting R = 4r,
[tex]V_L = \frac{k(Q - q)}{4r}[/tex]
Since [tex]V_S = V_L = V[/tex],
[tex]\frac{k(Q - q)}{4r} = \frac{kq}{r}[/tex]
=> 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
