Question

Consider a cube of sides a = 1.55 m, as shown in the diagram below. Suppose that an electric field is present and is given by E = bxⁿ, where b = 1.00 N/(Cmⁿ) and n = 2.3. Calculate the magnitude of the total charge within the cube.

Answer 1

The electric field points along the z-axis, so the electric flux, defined by $\phi$ = EA , is non-zero only for the top and bottom faces. But the bottom face at z = 0 has E = 0. Thus, all the flux comes from the top face. The electric field points into the cube (downward), which is opposite to the area vector for that top face so that the flux is negative. By Gauss