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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.)
Solution
Let θ is the angle between `vecm` and `vecB`
∴ Torque on magnetic dipole in a magnetic field B is
`τ = vecm vecB sin θ` ......(I)
Similarly of θ is the angle between electric dipole moment `vecp` and electric field E then torque on electric dipole in E is
`τ = vecp vecE sin θ` ......(II)
For if motion in I and II of electric and magnetic dipole are identical then τ' = τ
`vecp vecE sin θ = vecm vecB sin θ`
Or `vecpvecE = vecmvecB` .....(III)
We know that `vecE = veccvecB` (relation between E and B) ......(IV)
c is velocity of light
Put the value of E from IV in III
`vecpcB = vecmvecB`
| `vecp = vecm/c` |
It is the required relation.
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