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Magnetism And Matter — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsMagnetism And Matter5 Marks
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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