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 34.5 cm and is surrounded by dry air with a "breakdown" electric field of 4.20*10 6 V/m.

(a) What is the maximum potential of the dome? =..kV
(b) What is the maximum charge on the dome?..μC

Answer 1

Step-by-step explanation:

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Answer 2

a) Maximum potential of the dome = 724.5kV

b) Maximum charge on the dome = 13.9 micro Coulomb

Step-by-step explanation:

Diameter of the dome = 34.5 cm =34.5/100 = 0.345 m

Radius of the dome = Diameter/2 = 0.345/2 = 0.1725 m

Electric field strength, E = 4.20 * 10⁶V/m

a) Maximum potential of the dome, V = E*r

V = 4.20 * 10⁶ * 0.1725

V = 724500 Volts = 724.5kV

b) Maximum charge on the dome

V = kQ/r

Q = Vr/k

Q = (724500 * 0.1725)/(9*10⁹)

Q = 1.39 * 10⁻⁵C

Q = 13.9 micro Coulomb