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 $3.5\mu C$. 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

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

Radius of outer cylinder, $r_1=1.5cm=0.015m$

Radius of inner cylinder, $r_2=1.4cm=0.014m$

Charge on the inner cylinder, q= 3.5 µC

Capacitance of coaxial cylinder,

$C=\frac{2\pi {\epsilon }_{o}l}{ln\left(r_1/r_2\right)}$

$=1.2\times {10}^{-10}F$

Potential of the inner cylinder is given by,

$V=\frac{q}{C}$

$=2.92\times {10}^{4}V$