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  • A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 1 0 2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is th

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?

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best_answer

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 B2 be 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

Posted by

HARSH KANKARIA

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