Question

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).

Answer 1

Capacitance of cylinderical capacitor is given by, $\boxed{\bf{C=\frac{2\pi\epsilon_0L}{2.303log_{10}\frac{b}{a}}}}$

where, L is the length of cylinderical capacitor.a is inner radius of capacitor, b is outer radius of capacitor and $\epsilon_0$ is the permittivity of the space (vaccum).

given, L = 15cm = 0.15 m

a = 1.4cm = 0.014 m

b = 1.5 cm = 0.015 m

$\epsilon_0$ = 8.85 × 10^-12 C²/Nm²

so, capacitance of the cylinderical capacitor, C = $\frac{2\pi(8.85\times10^{-12})(0.15)}{2.303log_{10}\frac{0.015}{0.014}}$

= 1.21 × 10^-10 F

now electric potential of the inner cylinder is $\boxed{\bf{V=\frac{Q}{C}}}$

given, Q = 3.5 μC = 3.5 × 10^-6 C

so, V = 3.5 × 10^-6/(1.21 × 10^-10)

= 2.89 × 10⁴ V