3. Lightning Cloud ing cloud drifting overhead. At the earth\'s surface you meas

Question

3. Lightning Cloud ing cloud drifting overhead. At the earth's surface you measu re a vertical electric field of magnitude 100 Volts/meter. Suppose the bottom of the cloud is 300m above the earth surface and the top of the cloud is 600 m above the earth surface. The simplified charge distribution of the cloud is such that its total charge is zero, but it has charge -Q at the ver,y bottom, and charge +Q at the very top. (a) Estimate the magnitude of the charge Q. (b) Estimate the force on the cloud Hint: the earth's surface is a reasonably good ground plane.

Explanation / Answer

A) Electric field in between the clouds is E = (kQ/r1)-(-k*Q/r2)

E = k*Q*[(1/r1)+(1/r2)]

E = 9*10^9*Q*[(1/300)+(1/600)] = 100

9*10^9*Q*0.005 = 100

Q = 100/(9*10^9*0.005)

Q = 2.22*10^-6 C

b) Force is F = Q*E = 2.22*10^-6*100 = 2.22*10^-4 N

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