Question

Three point charges +q, –2q and +4q as shown in figure. The electric flux due to this configuration through the surface S is

Answer 1

Given that,

Inside charges are

$q_{1}=q$

$q_{2}=-2q$

Outside charge is

$q_{3} = +4q$

The charge enclosed by the surface is -2q, +q and +4q is not enclosed and will not be a part of flux through S.

The total charge will be

$Q=q_{1}+q_{2}$

Put the value into the formula

$Q=-2q+q = -q$

We need to calculate the electric flux due to this configuration through the surface S

Using formula of flux

$\phi=\dfrac{Q}{\epsilon_{0}}$

Put the value of total charge

$\phi=\dfrac{-q}{\epsilon_{0}}$

Hence, The electric flux due to this configuration through the surface S is $\dfrac{-q}{\epsilon_{0}}$