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

Length of a co-axial cylinder, l= 15 cm = 0.15 m

Radius of outer cylinder, r₁ = 1.5 cm = 0.015 m

Radius of inner cylinder,r₂ = 1.4 cm = 0.014 m

Charge on the inner cylinder, q = 3.5 μC = 3.5 x 10^-6 C

Capacitance of a co-axial cylinder of radii r₁  and r₂ is given by the relation

C = (2πε₀ l)/log_e(r_1/r₂)

Where,

ε₀= Permittivity of free space = 8.85 x 10⁻¹² N⁻¹m⁻² C²

Therefore C =2π (8.85 x 10⁻¹² x 0.15)/2.3026 log10 (0.15/0.14)

=2π (8.85 x 10⁻¹² x 0.15)/2.3026 0.0299

= 1.2 x 10⁻¹⁰ F

Potential difference of the inner cylinder is given by,

V=q/C = (3.5 x 10^-6) /(1.2 x 10⁻¹⁰)

=2.92 x 10⁴ V

2.3026×0.0299

Potential difference of the inner cylinder is given by,