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

Answers (1)

Given,

The magnitude of the first magnetic field, B1 = 1.2 × 10–2 T

The angle between the magnetic field directions, \theta = 60°

The angle between the dipole and the magnetic field B_{1} is \theta_{1} = 15°

Let Bbe the magnitude of the second magnetic field and M be the magnetic dipole moment

Therefore, the angle between the dipole and the magnetic field B2 is \theta_{2} = \theta - \theta_{1}= 45°

Now, at rotational equilibrium,

The torque due to field B1 = Torque due to field B2

MB_{1}sin\theta_{1}= MB_{2}sin\theta_{2}

 B_{2} = \frac{MB_{1}sin\theta_{1}}{Msin\theta_{2}} = \frac{1.2\times10^{-2}\times sin15\degree}{sin45\degree}

= 4.39 \times 10^{-3}T

Hence the magnitude of the second magnetic field = 4.39 \times10^{-3}T

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