Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A point charge of nC sits at the centre of a cube whose edges are m long. Find the net flux through the whole cube and through one face. A charge of nC is now placed at the same point, so that both charges are at the centre. What is the flux through one face now?
Gauss's law: the net flux through a closed surface is , with . Only the net charge inside counts. The shape and size of the surface do not matter. For a sphere of radius with the charge at its centre, .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The whole cube. .
Step 2. One face. The charge is at the centre, so all six faces are alike. .
Step 3. Both charges. The net charge inside is nC. The flux through the cube is . One face gets .
Answer: , and .
Check. The two charges together are nC, which is two thirds of nC. And . It fits.
Watch out. The edge of m is not needed. A cube twice as large gives the same fluxes.
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