Answer to Question #104809 in Electricity and Magnetism for 888

Question

A negatively charged particle is placed inside a spherical shell with positive charge distributed evenly on its surface. Draw the electric field lines at equilibrium state on the diagram

Answer 1

Assume that,

A negatively charged particle $-q_1$ is placed inside a spherical shell with positive charge $+q_2$ distributed evenly on its surface $(\lvert q_1\rvert=\lvert q_2\rvert=q)$ .

$\int EdA=\frac{1}{\epsilon_0}\sum{q_i}$

Electric field outside the shell

$E\cdot 4\pi r^2=\frac{1}{\epsilon_0}(-q+q)\to E=0$

Electric field inside the shell

$E\cdot 4\pi r^2=\frac{1}{\epsilon_0}(-q)\to E=\frac{-q}{4\pi\epsilon_0r^2}$

The field outside the shell depends on the magnitude of the charges $q_1$ and $q_2$ .