Answer to Question #216617 in Physics for Pearl

Question

Which of the following Maxwell's equation shows that there is no free magnetic poles? explain this. How do you think this particular equation will be modified if there are free magnetic poles

Answer 1

1. Which of the following Maxwell's equation shows that there is no free magnetic poles?

$$\oint\limits_S\mathbf{B}\cdot d\mathbf{s}=0$$

where $\mathbf{B}$ is the vector of the magnetic induction, and integration is pefrormed over some closed surface $S$. Since the left side of this equation denotes the flux of the magnetic induction field, the equation means that for any closed surface number of magnetic lines that go into the surface is equal to the number of magnetic lines that go out of the surface. Thus, there are not possible to isolate the sorce or the sink of the magnetic lines (free magnetic poles).

2. How do you think this particular equation will be modified if there are free magnetic poles?

It should be modified to be similar to the analogous equation for the electric field, that has free poles (charges):

$$\oint\limits_S\mathbf{B}\cdot d\mathbf{s}=Q_m$$

where $Q_m$ is some magnetic charge inside the closed surface $S$.