Chapter 21, Problem 91MSPP

A Lightning Strike

Storm clouds build up large negative charges, as described in the chapter. The charges dwell in charge centers, regions of concentrated charge. Suppose a cloud has –25 C in a 1.0|dash|km|dash|diameter spherical charge center located 10 km above the ground, as sketched in Figure P21.86. The negative charge center attracts a similar amount of positive charge that is spread on the ground below the cloud.

Figure P21.86

The charge center and the ground function as a charged capacitor, with a potential difference of approximately 4 × 10⁸ V. The large electric field between these two "electrodes" may ionize the air, leading to a conducting path between the cloud and the ground. Charges will flow along this conducting path, causing a discharge of the capacitor-a lightning strike.

If 12.5 C of charge is transferred from the cloud to the ground in a lightning strike, what fraction of the stored energy is dissipated?

A. 12%

B. 25%

C. 50%

D. 75%