Lightning can be studied with a Van de Graff generator, which consists of a sphe

Question

Lightning can be studied with a Van de Graff 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 22.3 cm and is surrounded by dry air with a "breakdown" electric field of 4.20 x 10^6 V/m. What is the maximum potential of the dome? What is the maximum charge on the dome?

Explanation / Answer

a) Field strength at the surface is V/r, where V is the potential and r the radius (ie 22.3/2 = 11.15 cm).
So V = E*r = 4.20*10^6 * 11.15*10^-2 = 468.3 kV
It must not exceed the breakdown field of air, or there will be a discharge.

b) V = kQ/r

Q = Vr/k =(468300*0.1115)/(9*10^9)

Therefore, Q= 5.80 micro coulomb

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