Question

a conducting cylinder of radius 3.25 cm and length 5.6 cm has a total charge of 4.5 x 10 c distributed uniformly on its surface area. find the potential at a) its surface, and b) 2.5 cm and c) 5.0 cm from the center of the cylinder.

Answer 1

The linear density of charge

$$\lambda=\frac{Q}{l}=\frac{45\:\rm C}{0.0325\:\rm m}=45\:\rm C/m$$

The potential of electric field from charged cylinder

$$V=2k\lambda\ln\frac{r}{r_0}$$

(a) $r=r_0$

$$V=0$$

(b) $r=2.5\:\rm cm$

Inside a conducting cylinder the field is constant and equal to the it's surface value. Hence

$$V=0$$

(c) $r=5.0\:\rm cm$

$$V=2*9*10^9*45*\ln\frac{5.0}{3.25}=152*10^9\;\rm V$$