Three charges of magnitude -2Q, -3Q and Q are located at (a, 0, 0), (3a, 0, 0) and (5a, 0, 0) respectively. What is the magnitude of electric flux due to these charges through a sphere of radius 4a with its centre at the origin?

$\frac{5Q}{ε_0}$

The correct answer is Option (2) → $\frac{5Q}{ε_0}$

Flux, $\phi=\frac{q_{enc}}{ε_0}$ [Gauss law]

where,

$q_{enc}$ = Net charge enclosed within the surface

$ε_0$ = Permittivity of free surface

Now,

The sphere has a radius of 4a, and its center at origin. Therefore, any charge located at a distance less than or equal to 4a from the origin will be enclosed within the sphere.

Given,

Charge −2Q at (a, 0, 0)

Charge −3Q at (3a, 0, 0)

Charge Q at (5a, 0, 0)

$q_{enc}=-2Q+(-3Q)$

$=-5Q$

∴ Using Gauss law,

$|\phi|=\frac{5Q}{ε_0}$