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Write the Maxwell鈥檚 equation.

$\begin{array}{l}鈭�鈰�\mathbf{E}\mathbf{=}\frac{蚁}{{\mathbf{脦}}_0}\text{鈥夆赌夆赌夆赌�}\left(Gauss\text{鈥�}law\right)\\ 鈭�脳E=0\\ 鈭�鈰�B=0\end{array}$

Write the amperes law

$鈭�鈰�\mathbf{B}\mathbf{=}{\mathbf{渭}}_0\mathbf{J}$

As the magnetic monopole exists then there will be no change in Ampere鈥檚 law and gauss law.

Actually $鈭�鈰�B=0$implies there will be no magnetic monopoles.Then if magnetic monopoles exist, then

$鈭�鈰�B={伪}_0{蚁}_m$

Here${蚁}_m$,is the density of magnetic change and${伪}_0$is the same constant.

Rewrite the Maxwell鈥檚 equation as

$鈭�脳E={尾}_0{J}_m$

Here, $J_m$is the magnetic current density and${尾}_0$is another constant.

Thus, magnetic charge is conserved. Hence, ${蚁}_m$and$J_m$satisfy continuity equation and is written as

$鈭�鈰�J_m+\frac{鈭�{蚁}_m}{鈭�t}=0$

Write the expression for force on magnetic monopole.

$F=q_m[B+(蠀脳E)]$

Consider both the equation directionally not correct.

Here, $E$has same units as$蠀B$ .

Hence, divide $蠀脳E$with dimensions of velocity squared and rewrite the equation as

$F=q_e[E+(蠀脳B)]+q_m[B鈭�\frac{1}{c^2}(蠀脳E)]$

Now, write the expression for magnetic field along the lines ofCoulomb鈥檚 law.

.

$F=\frac{{伪}_0}{4蟺}\frac{q_{m1}{q}_{m2}}{r^2}\widehat{r}$