A charge Q = 41.2 C sits somewhere inside a cube of side length l = 4.7 cm. A) W

Question

A charge Q = 41.2 C sits somewhere inside a cube of side length l = 4.7 cm.

A) What is the electric flux in Nm2/C through the surface of the cube?

B) Now assume the charge is at the very center of the cube. What is the flux through one of the faces, in Nm2/C?

C) A regular polyhedron is a three-dimensional object whose faces are all identical regular polygons - that is, all their angles and edges are the same. A cube is an example for n = 6 faces. If we put our charge at the center of a regular polyhedron with n faces, give an expression for the flux through a single face.

Explanation / Answer

a)

Qin = 41.2 uC

using gauss law ,

electric flux from the cube = Qin/(epsilon0)

electric flux from the cube = 41.2 *10^-6/(8.854 *10^-12)

electric flux from the cube = 4.63 *10^6 N.m^2/C

the electric flux from the cube is 4.63 *10^6 N.m^2/C

b)

due to symmetry

electric flux through one face = net electric flux/6

electric flux through one face = 4.63 *10^6/6

electric flux through one face = 7.76 *10^5 N.m^2/C

c)for n faces

the flux through a single face = Q/(n * epsilon0)

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