Answer to Question #308250 in Physics for Rich

Question

The radius of the outer sphere of a spherical capacitor is five times the radius of its 

inner shell. What are the dimensions of this capacitor if its capacitance is 5.00 pF?

Answer 1

The capacitance of a spherical capacitor is given by

$$C=\frac{1}{k\left(\frac{1}{R_1}-\frac{1}{R_2}\right)}$$

Hence

$$\frac{1}{R_1}-\frac{1}{R_2}=\frac{1}{kC}$$

$$\frac{1}{R_1}-\frac{1}{5R_1}=\frac{1}{kC}$$

$$\frac{4}{5R_1}=\frac{1}{kC}$$

$$R_1=\frac{4}{5}kC\\ =\frac{4}{5}*9*10^9*5.00*10^{-12}\\ =0.036\:\rm m=3.6\: cm$$

$$R_2=5R_1=5*3.6\rm\: cm=18\: cm$$