Question

A cylindrical capacitor has two co-axial cylinders of length 15 cmand radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and theinner cylinder is given a charge of 3.5 μC. Determine the capacitanceof the system and the potential of the inner cylinder. Neglect endeffects (i.e., bending of field lines at the ends).

Answer 1

Given: The length of a coaxial cylinder is 15 cm, the radius of outer cylinder is 1.5 cm, the radius of inner cylinder is 1.4 cm, the charge on the inner cylinder is 3.5 μC.

The capacitance of a coaxial cylinder is given as,

C= 2π ε 0 l log e r 1 r 2

Where, the length of a co-axial cylinder is l, the radius of outer cylinder is r 1 , the radius of the inner cylinder is r 2 .

By substituting the given values in above formula, we get

C= 2π×8.85× 10 −12 ×0.15 2.303 log 10 ( 0.15 0.14 ) = 2π×8.85× 10 −12 ×0.15 2.303( 0.0299 ) = 8.341× 10 −12 0.069 =1.2× 10 −10  F

The potential difference of the inner cylinder is given as,

V= q C

Where, the charge on the inner cylinder is q.

By substituting the given values in the above formula, we get

V= 3.5× 10 −6 1.2× 10 −10 =2.92× 10 4  V

Thus, the capacitance of the system is 1.2× 10 −10  F and the potential difference on the inner cylinder is 2.92× 10 4  V.