Question

A charge q is located above the centre of a square plate of side a, at a distance $\frac{a}{2}$. The flux of electric field through the plate Is?

• A. $\frac{q}{{ϵ}_0}$
• B. $\frac{q}{2{ϵ}_0}$
• C. $\frac{q}{4{ϵ}_0}$
• D. $\frac{q}{6{ϵ}_0}$

Answer 1

The correct option is D

$\frac{q}{6{ϵ}_0}$

Consider five more faces such that it forms a closed cube with ‘q’ at its centre.

Flux through this cube =$\frac{q}{{ϵ}_0}$

By symmetry, as the charge is symmetrically located.

${\varphi }_{oneface}=\frac{q}{6{ϵ}_0}=\frac{1}{6}Totalflux$

Hence (d).