Question

A point charge of17.7uc is located at centre of a cube of side 0.03m. find the electric flux through each face of cube

Answer 1

answer : (2/3) × 10^6 Nm²/C

According to Gauss theorem, electric flux through the gaussian surface is the ratio of charge enclosed inside the surface and permittivity of medium.

i.e., $\phi=\frac{q_{en}}{\epsilon_0}$.

here we used word gaussian surface, gaussian surface is an imaginary symmetrical surface drawn around the charge particle.

in question, cube is symmetrical solid shape. so, we can assume it is a gaussian surface . so net electric flux through the cube , $\phi=\frac{q_{en}}{\epsilon_0}$.

= $=\frac{Q}{\epsilon_0}$.

we know, cube has six identical faces.

so, electric flux through each face = $\frac{\phi}{6}$.

= $=\frac{Q}{6\epsilon_0}$.

now putting value of Q = 17.7uC = 17.7 × 10^-6 C

and $\epsilon_0$ = 8.85 × 10^-12 C²/Nm²

now, electric flux through each face of cube = 17.7 × 10^-6/(6 × 8.85 × 10^-12)

= 2 × 10^6/3

= (2/3) × 10^6 Nm²/C