A cube has one corner at the origin and the opposite corner at the point (L,L,L). The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by vector{E} = (a+b x){x^} + c{y^}

A) Find the total electric flux Phi_E through the surface of the cube.

B) What is the net charge q inside the cube?

### 2 Answers

0) density of charge is 1/εo ∂/∂x Ex = b/εo

B) Net charge is Q = b/εo L³

A) Electric flux is Φ = εo Q = bL³

the answer is A. Acc to gauss law electric field * total surface area= charge enclosed/epsilon. Now consider a cube. Charge inside the cube is ‘q’. Total surface of cube is 6*a*a(a is length of edge of cube). The total flux through the cube is q/epsilon. q/epsilon is the flux for 6 faces. Therefore for one face the flux will be 1/6*q/epsilon. 8