Question

A cylindrical capacitor consists of a cylinder (of length L and radius a) with a total charge Q nested inside a thin conducting cylindrical shell (of length L and radius b) with total charge

Answer 1

cylindrical capacitor. Suppose that our capacitor is composed of an inner cylinder (plate) with radius a enclosed by an outer cylinder (plate) with radius b.

Since we know that the basic relationship Q = CV, we must obtain expressions for Q and V to evaluate C.

We will use Gauss' Law to evaluate the electric field between the plates by using a gaussian surface that is cylindrical in shape of length L.

Since our cylinders have a uniform charge distribution,

If a positive test charge were to be moved between the plates, from A to B, its electric potential energy (EPE) would decrease while its kinetic energy (KE) would increase.

Multiplying through by negative 1 yields:

Returning to Q = CV

In this derivation a is inner radius and b is outer radius.

Accrding given problm, b is inner radius and a is outer radius.

so, C = 2*pi*epsjilon*L/( ln(a/b) ). <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<---------------------------Answer

Note : Capacitance of any capacitor does not depend on charge on it.It depends only the geometry of the capacitor.