Question

You make a Gaussian surface surrounding a charge +Q, then you make a bigger Gaussian surface around the charge, whose area is three times bigger. The electric flux through the bigger surface is

A.) nine times larger than the flux of electric field through the smaller Gaussian surface.

B.) unrelated to the flux of electric field through the smaller Gaussian surface.

C.) three times smaller than the flux of electric field through the smaller Gaussian surface.

D.) three times larger than the flux of electric field through Gaussian surface B.

E.) equal to the flux of electric field through the smaller Gaussian surface

Answer 1

Correct Answer: E. equal to the flux of electric field through the smaller Gaussian surface.

According to Gauss law, the electric flux passing through a close surface is proportional to the charge enclosed inside the surface and is not dependent on the size of Gaussian surface.

Also, Electric flux is represented by the number of electric field lines passing through an area. If we consider a close the surface area around a charge then the number of field lines starting from the charge will pass through the close surface and the number of field lines will be the same irrespective of the size of the surface. Another way to understand this is by considering electric flux as a dot product of electric field and area. If we have a bigger surface area, then the radius is larger. At a larger radius the electric field is weaker. So when we multiply field with area we end up with the same answer as the answer we would get for a smaller Gaussian surface (for which field is larger but area is smaller)