P27_003.PDF

3. Suppose the charge on the sphere increases by ∆ q in time ∆ t . Then, in that time its potential increases

∆ q

4 πε 0 r

∆ V =

where r is the radius of the sphere. This means

∆ q =4 πε 0 r ∆ V.

Now, ∆ q =( i in −

i out )∆ t ,where i in is the current entering the sphere and i out is the current leaving.

Thus,

∆ t =

∆ q

i in −

i out = 4 πε 0 r ∆ V

i in −

i out

(0 . 10m)(1000V)

1 . 0000000A) =5 . 6

10 − 3 s .

(8 . 99

10 9 F / m)(1 . 0000020A

−