Question

Lightning can be studied with a Van de Graaff generator, which consists of a spherical dome on which charge is continuously deposited by a moving belt. Charge can be added until the electric field at the surface of the dome becomes equal to the dielectric strength of air. Any more charge leaks off in sparks. Assume the dome has a diameter of 25.0 cm and is surrounded by dry air with a "breakdown" electric field of 3.00 10^6 V/m.

Required:
a. What is the maximum potential of the dome?
b. What is the maximum charge on the dome?

Answer 1

(a) V = 3.75 x 10^5 V

(b) q = 5.2 x 10^-6 C

Step-by-step explanation:

Diameter, d = 25 cm

radius, r = 12.5 cm = 0.125 m

Electric field, E = 3 x 10^6 V/m

(a) The maximum potential is given by

`V = E * r \\\\V = 3* 10^6* 0.125\\\\V = 3.75*10^5 V`

(b) The charge is given by

`V = (k q)/(r)\\\\3.75*10^5=(9*10^9* q)/(0.125)\\\\q = 5.2* 10^(-6) C`