Question

To practice Problem-Solving Strategy 22.1: Gauss's Law.An infinite cylindrical rod has a uniform volume charge density rho(where rho>0). The cross section of the rod has radius r0. Find the magnitude of the electric field E at a distance r from the axis of the rod. Assume that r

Answer 1

Answer:

Solution for 3 different cases are given in explanation.

Explanation:

Gauss's Law:

$\int_S E.dA=Q_{encl}/\epsilon_0$

for $r$ :

$E.2\pi rL=\frac{\rho\pi r^2L/\pi r_0^2}{\epsilon_0} \\\\E=\frac{\rho r}{2\pi\epsilon_0 r_0^2}$

for $r=r_0$ :

$E.2\pi r_0L=\frac{\rho\pi r_0^2L}{\epsilon_0} \\\\E=\frac{\rho r_0}{2\epsilon_0}$

for $r>r_0$ :

$E.2\pi rL=\frac{\rho\pi r_0^2L}{\epsilon_0} \\\\E=\frac{\rho r_0^2}{2\epsilon_0 r}$