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Chapter 4: Q58P (page 812)

The charge center of a thundercloud, drifting 3.0km above the earth鈥檚 surface, contains 20C of negative charge. Assuming the charge center has a radius of 1.0km, and modeling the charge center and the earth鈥檚 surface as parallel plates, calculate: (a) the capacitance of the system; (b) the potential difference between charge center and ground; (c) the average strength of the electric field between cloud and ground; (d) the electrical energy stored in the system.

Short Answer

Expert verified

(a) C=9.27nF

(b)VCG=2.16GV

(c)E=7.2脳105V/m

(d)U=21.6GJ.

Step by step solution

01

Parameters.

d=3.0km=3.0脳103mQ=20Cr=1km=1脳103m

02

(a) Calculating the capacitance of the system.

The capacitance is given by

C=鈭�0Ad (1)

All is known except A so consider the cloud to be a circular disk and the area is given by

A=蟺r2=3.14脳106m2

Substituting in (1) yields

C=8.85x10-12脳3.14脳10630脳103=9.27脳10-9F.

03

(b) Calculating the potential difference between the charge center and ground.

The voltage difference between the cloud and the ground is given by

VCG=QC=209.27脳10-9=2.16脳109V.

04

(c) Calculating the average strength of the electric field.

The electric field flows through the air is given by

EA=Q鈭�0鈬�E=QA鈭�0 (3)

Substituting in (3) yields

E=208.85脳10-12脳3.14脳106=7.2脳105V/m

05

(d) Calculating the electrical energy stored in the system.

The energy stored in system is given buy

U=12QV=12脳20脳2.16脳109=2.16脳1010J.

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Fig. E25.33

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