Answer to Question #193015 in Physics for Anne

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

Radius of the outer shell: R=5r

Radius of the inner shell: r

Solution

The capacitance is

$$C=\frac{4\pi\epsilon_0}{1/r-1/(5r)}=5\pi\epsilon_0r,\\\space\\ r=\frac{C}{5\pi\epsilon_0}=0.036\text{ m},\\\space\\ R=0.18\text{ m}.$$