Suppose we want to verify the analogy between electrostatic and m… - Vidyadip

Question

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

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Answer

Electric field $\vec{\text{E}}$ and magnetic field $\vec{\text{B}}$ are related as
Key concept: Suppose the angle between $\vec{\text{p}}$ and $\vec{\text{E}}$ is $\theta$. Torque on electric dipole of moment $\vec{\text{p}}$ in an electric firld $\vec{\text{E}},\tau=\text{pE}\sin\theta.$
Let us assume that the angle between $\vec{\mu}$ and $\vec{\text{B}}$ is $\theta$.
Torque on magnetic dipole moment $\vec{\mu}$ in magnetic field $\vec{\text{B}}$,
$\vec{\tau}=\mu\text{B}\sin\theta\ \hat{\text{n}}$
If these two motions are identical, then
$\text{pE}\sin\theta=\mu\text{B}\sin\theta$
$\Rightarrow\ \text{pE}=\mu\text{B}\ .....{\text{i}}$
But, $\text{E}=\text{cB}$
$\therefore$ Putting this value in Eq. (i),
$\text{pcB}=\mu\text{B}$
$\Rightarrow\ \text{p}=\frac{\mu}{\text{c}}$

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