Question

(a) State Gauss' law for magnetism.
(b) How this differs from Gauss' law for electrostatics?
(c) Why is the difference in the two cases?

Answer 1

a) Gauss' Law for magnetism applies to the magnetic flux through a closed surface. In this case the area vector points out from the surface. Because magnetic field lines are continuous loops, all closed surfaces have as many magnetic field lines going in as coming out. Hence, the net magnetic flux through a closed surface is zero.

Net flux $\varphi =\int B.dA=0$

b) Gauss' Law for electrostatics is a very useful method for calculating electric fields in highly symmetric situations. Gauss' Law for magnetism is considerably less useful.

c) There is a difference in both laws because the magnetic field-lines behave in a quite different manner to electric field-lines, which begin on positive charges, end on negative charges, and never form closed loops. Incidentally, the statement that electric field-lines never form closed loops follows from the result that the work done in taking an electric charge around a closed loop is always zero. This clearly cannot be true if it is possible to take a charge around the path of a closed electric field-line.