Lightning can be studied with a Van de Graaff generator, which consists of a sph

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 as shown in the figure below. Assume the dome has a diameter of 44.0 cm and is surrounded by dry air with a "breakdown" electric field of 3.00 106 V/m.

(a) What is the maximum potential of the dome?

__________kV

(b) What is the maximum charge on the dome?

___________C

Explanation / Answer

2. Electric field = 3*10^6 V/m

diameter of dome = 44.0 cm = 0.44 m

r = 0.22 m

at the surface of spherical conductor

E = k*Q/r^2

Q = E*r^2/k

Q = 3*10^6*0.22^2/(9*10^9)

Q = 1.613*10^-5 C

Q = 16.13*10^-6 C = 16.13 uC

1.

at surface

V = kQ/r

V = 9*10^9*16.13*10^-6/0.22

V = 659.87*10^3 V = 659.87 kV

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