Question

If magnetic monopoles would have existed. how would gauss's law of magnetism be modified?

Answer 1

Gauss law:

1. This law for magnetism states that the magnetic flux across any closed curve or surface is zero.
2. This law is consistent with the observation that isolated magnetic poles (monopoles) do not exist.
3. Gauss’s law for magnetic fields in the integral form is given by:
4. ${\oint }_s\overrightarrow{B}.da=0$, Where $\overrightarrow{B}$= magnetic flux, $s$= an arbitrary closed surface.
5. Gauss's law for magnetism states that no magnetic monopoles exist and that the total flux through a closed surface must be zero.
6. Gauss's law for the electric field describes the static electric field generated by a distribution of electric charges.
7. It states that the electric flux through any closed surface is proportional to the total electric charge enclosed by this surface.

Magnetic monopoles

1. Also, the magnetic monopole does not exist, thus magnetic field lines form closed loops.
2. So the number of field lines going out through the closed surface is equal to the number of field lines coming in.
3. Hence magnetic flux linked with a closed surface is always zero.
4. A magnetic monopole, if it exists, would have the defining property of producing a magnetic field whose monopole term is non-zero.
5. A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion.

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Effect on Gauss law:

1. As we clearly see from the statement of gauss law that no monopoles exist.
2. This law is consistent with the observation that isolated magnetic poles (monopoles) do not exist.
3. A magnetic monopole needs to be analogous to an electric monopole.
4. A stationary electric monopole produces no magnetic field, so a magnetic monopole can produce no electric field.
5. Therefore Gauss's law for electricity is unaffected,

Thus we conclude that as there are no monopoles, modification of gauss law leads to an analogous form.