Gaussian Cube Flux
Minimum and Maximum Flux?
Help with Flux Max and Min?
A particle with charge q is located inside a cubical gaussian surface. No other charges are nearby. If the particle is at the center of the cube, what is the flux through each one of the faces of the cube?
0
q/epsilon
q/(2epsilon)
q/(4epsilon)
q/(6epsilon)
q/(8epsiolon)
depends on the size of the cube
If the particle can be moved to any point within the cube or on its surface what maximum and minimum values can the flux approach. Thanks in advance for helping!
Total flux phi = q/e
By symmetry, phi for one side of a cube when charge is centered = q/(6e)
If you move the charge to the center of one side, phi for that side = q/(2e), and phi for the opposite side = q/(24e) (centered value divided by distance ratio^2). With the charge in a corner you also get q/(24e) on each of the three farthest sides, since the three sides subtend a total solid angle of 1/8 sphere from the corner.
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