A cylindrical capacitor has an inner conductor of radius 2.7 and an outer conductor of radius 3.1 . The two conductors are separated by vacuum, and the entire capacitor is 3.0 mm 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.

(A) Capacitance per unit length =

(B) The magnitude of charge on both conductor is C and the sign of charge on inner conductor is and the sign on outer conductor is

Explanation:

Given :

Radius of inner part of conductor   = m

Radius of outer part of conductor   = m

The length of the capacitor = m

(A)

Capacitance is purely geometrical property. It depends only on length, radius of conductor.

From the formula of cylindrical capacitor,      

Where,

But we need capacitance per unit length so,

capacitance per unit length =

(B)

The charge on both conductors is given by,

Where, C = capacitance of cylindrical capacitor and value of F, V

∴ C

The magnitude of charge on both conductor is same as above but the sign of charge is different.

Charge on inner conductor is and Charge on outer conductor is .

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