Question 21

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60º, and one of the fields has a magnitude of 1.2 x 10^{-2}T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field?

Answer

Magnitude of one of the magnetic fields, *B*_{1}= 1.2 × 10 ^{- 2 }T

Magnitude of the other magnetic field = *B*_{2}

Angle between the two fields, *θ*= 60°

At stable equilibrium, the angle between the dipole and field *B*_{1}, *θ*_{1}= 15°

Angle between the dipole and field *B*_{2}, *θ*_{2}= *θ* - *θ*_{1} = 60° - 15° = 45°

At rotational equilibrium, the torques between both the fields must balance each other.

∴Torque due to field *B*_{1}= Torque due to field *B*_{2}

*MB*_{1}sin*θ*_{1}= *MB*_{2}sin*θ*_{2}

Where, *M*= Magnetic moment of the dipole

Hence, the magnitude of the other magnetic field is 4.39 × 10 ^{- 3}T.

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