Question

Four charges are located on the comers of a square. The sides of the square have a length of 0.05m. The upper left comer has a charge of q. The upper right comer has a charge of -q. The lower left comer has a charge of 2q. The lower right comer has a charge of -2q. If the magnitude of q is 1 .0 times 10 -7C, find the magnitude of the force exerted on the charge at the lower left comer of this system. A point charge q is placed at one comer of edge a. What is the electric flux through each of the cube faces?

Answer 1

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nC a 12-5004. = 12.50 % 3.536 g 2 2. /20
Since by Gauss law we have:
phi(flux)=q/epsilon
This is the flux linked with a closed surface(complete)In this case what you have to do is that you'll have to manually think that in which direction/face the flux is not zero.
Imagine a cube with charge q at one of its corner ,now place another cube besides it touching one of its sides(such that two faces exactly meet each other), now similarly place two more cubes beneath these two,now you get 4 cubes,the corner charge is still not fully covered its visible from one side, place 4 more cubes in a similar fashion to cover the charge completely. now by the formula, the flux linked with the whole structure(now a closed surface) is =q/epsilon not, but the flux linked with one cube will be = 1/8 *q/(epsilon) because flux has been distributed to 8 cubes symmetrically.
but even in One(original)cube. You should be able to see electric field lines originating radially outwards from the cornered charge in every direction, but note that these lines run parallel to(don't penetrate) at least 3 faces(two on the sides on at the bottom), so that means the flux linked with one cube is distributed only to 3 faces in it. So I think the flux linked with one face will be 1/3 of flux linked with one cube i.e
=1/3* 1/8 * q/epsilon
=1/24 * q/epsilon