Question

(a) Define electric flux. Is it a scalar or a vector quantity ? A point charge q is at a distance of d/2 directly above the centre of a square of side d, as shown in the figure. Use Gauss' law to obtain the expression for the electric flux through the square.

(b) If the point charge is now moved to a distance 'd' from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.

Answer 1

(a) Electric flux : Electric flux through an area is defined as the number of electric field lines passing in a unit area. It is a scalar quantity.
Imagine a cube of edge d, enclosing the charge. The square surface is one of the six faces of this cube. According to Gauss' theorem in electrostatics,

Total electric flux through the cube = $\frac{q}{{ϵ}_0}$

$\therefore$ Electric flux through the square surface = $\frac{q}{6{ϵ}_0}$

(b) On moving the charge to distance d from the centre of square and making side of square 2d, the flux does not change at all because flux is independent of side of square or distance of charge in this case.