Question

A research of Van de Graaff generator has a 2.50 mm diameter sphere with a charge of 6.00 µC on it. A. What is the potential near its surface? B. At what distance from its center is the potential 1.50 MV?​

Answer 1

Given info : A research of Van de Graaff generator has a 2.50 mm diameter sphere with a charge of 6.00 µC on it.

To find :

1. what is the potential near its surface ?
2. at what distance from its centre is the potential 1.5 MV ?

solution : radius , r = 2.50/2 = 1.25 mm = 1.25 × 10¯³ m

charge , q = 6 × 10¯⁶ C

now potential near its surface, V = kq/r

= (9 × 10^9 × 6 × 10^-6)/(1.25 × 10^-3)

= 54/1.25 × 10^6 volts

= 43.2 MV

let R distance from the centre is potential 1.5 MV

so. potential due to sphere, V' = Kq/R

⇒1.5 MV = (9 × 10^9 × 6 × 10^-3)/R

⇒1.5 × 10^6 = 54 × 10^6/R

⇒R = 54/1.5 = 36 m

Therefore 36 m from the centre of sphere, is the potential 1.50 MV