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In a region of space the electric field is given by E = E0 * i-hat + E0 * y * j-hat. Consider an imaginary cube of edge length a with its faces parallel to the coordinate planes (with one corner at the origin). Select the correct statement(s).
- The total electric flux through the two faces perpendicular to the x-axis is E0*a³.
- The net charge enclosed inside the cube is 2*epsilon0*E0*a³.
- The total electric flux through the two faces perpendicular to the y-axis is 2*E0*a³.
- The net charge enclosed inside the cube is epsilon0*E0*a³.
Correct answer: The net charge enclosed inside the cube is epsilon0*E0*a³.
Solution
The x-component E0 is uniform so its net flux through the x-faces is zero. The y-component E0*y gives flux E0*a*a² = E0*a³ through the top y-face and 0 through the bottom; net flux = E0*a³. By Gauss's law, Q_enc = epsilon0 * E0 * a³. Option A (x-faces flux = E0*a³) is wrong (it is zero). Option C (y-faces flux = 2*E0*a³) is wrong (it is E0*a³). Option D is correct.
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