Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of
$(i)$ electric dipole $\vec{p}$ in an electrostatic field $\vec{E}$ and
$(ii)$ magnetic dipole $\vec{M}$ in a magnetic field $\vec{B}$. Write down a set of conditions on $\vec{E}, \vec{B}, \vec{p}, \vec{M}$ so that the two motions are verified to be identical. (Assume identical initial conditions.)

(D) The torque on an electric dipole $\vec{p}$ in an electric field $\vec{E}$ is given by $\vec{\tau}_e = \vec{p} \times \vec{E}$,with magnitude $\tau_e = pE \sin \theta$.
The torque on a magnetic dipole $\vec{M}$ in a magnetic field $\vec{B}$ is given by $\vec{\tau}_m = \vec{M} \times \vec{B}$,with magnitude $\tau_m = MB \sin \theta$.
For the motions to be identical,the torques must be equal for the same angular displacement $\theta$,implying $\tau_e = \tau_m$.
Thus,$pE \sin \theta = MB \sin \theta$,which simplifies to $pE = MB$.
Using the relation between electric and magnetic fields in electromagnetic waves,$E = cB$,where $c$ is the speed of light.
Substituting $E = cB$ into the equation $pE = MB$,we get $p(cB) = MB$.
Therefore,the condition for identical motion is $p = \frac{M}{c}$ and the fields must be related by $E = cB$.