# Find the net electric flux through the spherical closed surface shown in the figure below.

Find the net electric flux through the spherical closed surface shown in the figure below. The two charges on the right are inside the spherical surface. (Take q1 = +1.98 nC, q2 = +1.06 nC, and q3 = -3.06 nC.)
N · m2/C

asked Feb 10, 2012 in Physics

To fine the electric flux through the closed surface we use Gauss's law, which states that the net electric flux through any closed gaussian surface is equal to the net charge inside the surface divided by the permittivity of free space.

Therfore:

electric flux = (charge in) / (permittiivity of free space)

(*permittivity of free space = 8.8542*10^-12 C^2/N*m^2 )

The charge outside the sphere is not needed to calculate the electric flux and can be ignored.

To begin, first find the net charge inside the sphere:

net charge inside = q2 + q3

where,

q2 =  +1.06 nC, and q3 = -3.06 nC.

and so,

net charge inside = +1.06 nC + -3.06 nC = 2nC  = 2*10^-9 C

Now just plug values back into Gauss's Law and get:

electric flux = (2*10^-9 C) / (8.8542*10^-12 C^2/N*m^2 )  =  -225.88N·m2/C

electric flux =  -225.88 N·m2/C

answered Feb 16, 2012 by ~Expert~ (3,856 points)
selected Feb 16, 2012 by awesome