Question

Find the flux of the electric field through a spherical surface of radius R due to a charge of 10⁻⁷ C at the centre and another equal charge at a point 2R away from the centre (figure 30-E2).

Answer 1

Given:

Let charge Q be placed at the centre of the sphere and Q' be placed at a distance 2R from the centre.

Magnitude of the two charges = 10⁻⁷ C

According to Gauss's Law, the net flux through the given sphere is only due to charge Q that is enclosed by it and not by the charge Q' that is lying outside.

So, only the charge located inside the sphere will contribute to the flux passing through the sphere.

Thus,
$$\begin{gathered} \varphi =\int \overrightarrow{E}.d\overrightarrow{s}\mathit{=}\frac{Q}{{\mathit{\in }}_{\mathit{0}}}=\frac{{10}^{-7}}{8.85\times {10}^{-12}} \\ \Rightarrow \varphi =1.1\times {10}^4{\mathrm{Nm}}^2{\mathrm{C}}^{-1} \end{gathered}$$