Question

The radius of the outer spear of a spherical capacitor is five times the radius of its inner shell . What are the dimensions of these capacitor if its capacitance is 5.00 picofarad?

Answer 1

The capacitance is given by

$$C=4\pi\epsilon_0(R_2*R_1)/(R_2-R_1)$$ $$R_2=5R_1$$

So

$$5.00*10^{-12}=4*3.14*8.85*10^{-12}\frac{5R_1^2}{4R_1}$$ $$R_1=0.0360\:\rm m=3.60\:\rm cm$$ $$R_2=5R_1=18.0\:\rm cm$$