Question

A cylindrical capacitor has an inner conductor of radius 2.2 mm and an outer conductor of radius 3.5 mm. The two conductors are separated by vacuum, and the entire capacitor is 2.8 m long.

(a) What is the capacitance per unit length?

(b) The potential of the inner conductor is 350 mV higher than that of the outer conductor. Find the charge (magnitude and sign) on both conductors.

Short answer

The capacitance per unit length is $120.0pF/m$.

The charge of the inner conductor is Q = +118pC and outer conductor is Q - 118pC

Step-by-step solution

About capacitance per unit length.

The potential V between the cylinders is not affected by the presence of

the charged outer cylinder and the capacitance per unit length C/L is given by

Now we can plug our values forandinto equation(1)

Hence, the capacitance per unit length is 120.0pF/m.

Calculation of charge when potential is given.

We are given the potential of the inner conductor V = 350 mV and higher than that of the outer conductor, which means the positive charge is on the inner conductor and the negative charge is on the outer conductor. To find the charge Q we can use the equation

Hence, the charge of the inner conductor is Q = +118pC and outer conductor is Q - 118pC.