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.)

Answer 1

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.