Find the electric flux through the surface of a sphere containing 15 protons and

Question

Find the electric flux through the surface of a sphere containing 15 protons and 10 electrons. Does the size of the sphere matter? If we changed the sphere to a box containing the same charge, would this matter? A cube of side L contains a flat plate with variable surface charge density of sigma(x, y) = -3xy. If the plate extends from x = 0 to x = L and from y = 0 to y = L, what is the total electric flux through the walls of the cube? A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density phi (r) is given by phi (r) = alpha r^n for r lessthanorequalto R phi (r) = 0 for r > R Here n > -3 and alpha is a positive constant having units of C/m^n. a) Determine alpha in terms of Q, R, and n. b) Using Gauss's Law, derive an expression for the magnitude of E vector as a function of r. Do this separately for both regions (r lessthanorequalto R and r > R), and your answers will be in terms of r, R, Q and epsilon_0. c) Why must n > -3?

Explanation / Answer

1) By Gauss law, Flux through the surface = q/e0

= (15*1.6e-19 - 10*1.6e-19) / 8.85e-12

= 9.04*10^-8 Nm^2 /C

Size does not matter. It only depends on charge enclosed.

Even if we take a box instead of sphere it would be same.

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