Question

How does Gauss law of magnetism explains the concept of absence of magnetic monopoles?

Answer 1

Dear student

Gauss's law for magnetism is $\varphi =∯\overrightarrow{B·}\overrightarrow{dS}$ where $\varphi$ is the flux through the closed surface dS but since magnetic field lines are continuous loops, all closed surfaces have as many as magnetic field lines going in as coming out. Hence, net magnetic flux through a closed surface is zero i.e. ​$\varphi$=0. This is equivalent to say that no monopole exits.
So if there exists monopole we can make a closed surface around that and find nonzero flux but as $\varphi$ is always zero for magnetic fields so this suggest no monopole.