A charge of 4mu C is placed at the origin Consider the net f

A charge of 4mu C is placed at the origin. Consider the net flux through a Gaussian sphere of radius 4cm and another sphere of radius 6cm, both centered on the charge. Which of the two spheres would have the larger flux, if any? Explain your reasoning.

Solution

Any flux that comes out of the smaller sphere will pass through the larger sphere

Flux = EA

E = electric field

A = area

E1A1 = E2A2

As the total charge is constant, the larger sphere has larger area but the charge spread out more and more with surface area. The charge density, the charge per unit area, decreases. Therefore the electric field decreases with increasing surface area. Hence the flux will remain constant.