Calculate the total electric flux leaving the cubical surface formed by the
six planes x, y, z = ±5 if the charge distribution is: (a) twopoint charges, 0.1 μC
at (1,−2, 3) and 17μC at (−1, 2,−2); (b) a uniform line charge of π μC/m at
x = −2, y = 3; (c) a uniform surface charge of 0.1 μC/m2 on the plane y = 3x.

Question

Calculate the total electric flux leaving the cubical surface formed by the
six planes x, y, z = ±5 if the charge distribution is: (a) twopoint charges, 0.1 μC
at (1,−2, 3) and 17μC at (−1, 2,−2); (b) a uniform line charge of π μC/m at
x = −2, y = 3; (c) a uniform surface charge of 0.1 μC/m2 on the plane y = 3x.

anonymous · Answer

using Gauss' law simplifies the question into trivial maths.
just take a Gaussian surface of the cube of length 5, and do the integral
$$\oint\limits \vec E \cdot \vec A =\Psi_{E(net)}=\frac{Q_{total}}{\epsilon_0 }$$
so, just check if the point charges are within the boundary and sub them into the $Q_{total}$.
in the case of the line and surface charge, you need to do an integral over the boundary of the Gaussian surface to find the enclosed charge.

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