Question

A cylindrical shell of radius 7.00 cm and length 2.40 m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the net charge on the shell and (b) the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.

Answer 1

For a cylindrical shell

$E\cdot 2\pi r\cdot l=\frac{(q/L)l}{\epsilon_0}\to E=\frac{q}{2\pi L\epsilon_0r}$

a) $q=2\pi L \epsilon_0 rE=2\cdot 3.14\cdot 2.4\cdot8.85\cdot10^{-12}\cdot0.07\cdot36000=336\cdot10^{-9}(C)$. Answer

b) According to Gauss's theorem $E\cdot 2\pi r\cdot l=\frac{0}{\epsilon_0}\to E=0$. Answer