An isolated conducting sphere has a 16 cm radius. One wire carries a current of 1.0000020 A into it. Another wire carries a current of 1.0000000 A out of it. How long would it take for the sphere to increase in potential by 1260 V?

It takes 11.20 ms for the sphere to increase in potential by 1260 V

Explanation:

Using the formula q = It where I is current in Ampere, and t is in seconds

q = (1.000002 - 1.0000000) t

q = 0.000002t

Voltage on the surface of the sphere V = Kq / r

where K is 9.0 * 10⁹ N². m² / c² and

R = 16 cm = 16 / 100 = 0.16m

V = Kq / r

substitute the value into q

V = K (0.000002t) / r

cross multiply

rV = K * 0.000002t

make t subject of the formula

t = 0.16 * 1260 / (9*10⁹ * 0.000002)

t = 201.6 / (18 * 10³)

t = 0.0112 s

= 11.20 ms

It takes 11.20 ms for the sphere to increase in potential by 1260 V