(a) Define electric flux. Is it a scalar or a vector quantity? A point charge q is at a distance of 2d directly above the centre of a square of side d, as shown in the figure. Use Gauss's 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.
Solution
(a) Electric flux is a scalar, ϕ=E⋅ΔS. Imagine the charge q at the centre of a cube of side d; the square is one of its six faces. By symmetry the total flux ε0q divides equally among the six faces:
ϕ=6ε0q
(b) With the charge at distance d and side 2d, the square is again one face of a cube of side 2d centred on the charge. The same symmetry gives 6ε0q — the flux is unchanged.
