During a lightning flash, there exists a potential difference of V cloud - V gro

Question

During a lightning flash, there exists a potential difference of Vcloud - Vground = 2.8 x 109 V between a cloud and the ground. As a result, a charge of -29 C is transferred from the ground to the cloud.

(a) How much work Wground–cloud is done on the charge by the electric force?

(b) If the work done by the electric force were used to accelerate a 1100-kg automobile from rest, what would be its final speed?

(c) If the work done by the electric force were converted into heat, how many kilograms of water at 0 °C could be heated to 100 °C?

Wground–cloud =

Explanation / Answer

a) Work done by an electric field is given by

W = qV

W = 29 X 2.8 X 109

W = 8.12 X 1011 J

b) The work done by electric field will be converted into the kinetic energy of the automobile

W = (1/2) mv2

8.12 X 1011 = (1/2) (1100)v2

v = 3.84 X 104 m/s

c)The work done will be converted to heat

W = ms(T2 - T1)

8.12 X 1011 = m (4.184 J/goC)(100 - 0)

m = 1.941 X 109 g

m = 1.941 X 106 Kg

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