A cubic cardboard box of side a = 0.310 m is placed so that its edges are parall

Question

A cubic cardboard box of side a = 0.310 m is placed so that its edges are parallel to the coordinate axes, as shown in the figure. There is NO net electric charge inside the box, but the space in and around the box is filled with a nonuniform electric field of the following form: E(x,y,z) = Kz j + Ky k, where K= 3.20 N/C.m is a constant.

1.What is the electric flux through the top face of the box? (The top face of the box is the face where z=a. Remember that we define positive flux pointing out of the box.)

2.What is the total electric flux through the five other faces of the box? (Again, outward flux is positive.)

Explanation / Answer

a = 0.31m, E(x, y, z) = 3.2z i +3.2y k

the area element of top face dA = dx dy

the normal of the face is n = k

the flux = ?0a?0a Ez dx dy = ?0a?0a 3.2 y dx dy = 3.2*a2/2 * a = 0.0476656 Nm2/C

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