Question

Two charges of magnitudes: -$2\mathrm{q}$ and $+\mathrm{q}$ are located at points $(\mathrm{a},0)$ and $(4\mathrm{a},0)$, respectively. What is the flux through the sphere of radii $3\mathrm{a}$ with centre as the origin due to the charges?

Answer 1

Step 1: Given data

Two charges of magnitudes: -$2\mathrm{q}$ and $+\mathrm{q}$

Points $(\mathrm{a},0)$ and $(4\mathrm{a},0)$

Radii $3\mathrm{a}$

Step 2: Derivation

Gauss's law:

Flux, $\left(\mathrm{\varphi }\right)=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

Here,

q is the total charge inside the surface of the sphere

Here,

$\mathrm{q}=-2\mathrm{Q}$ and the gaussian surface is a sphere of radius $3\mathrm{a}$ and center at the origin.

So,

Flux, $\left(\mathrm{\varphi }\right)=-\frac{2\mathrm{Q}}{{\mathrm{\epsilon }}_0}$

Here, flux is only due to charge$-2\mathrm{Q}$ because no. of field lines that enter the sphere due to charge $+\mathrm{Q}$ is equal to no. of field lines coming out of the sphere, so net flux is zero due to charge $+\mathrm{Q}$.