A magnetic dipole is under the influence of two magnetic fields.

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asked Jan 5, 2018 in Physics by sforrest072 (157,439 points) 61 410 940

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 × 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?

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answered Jan 5, 2018 by mdsamim (213,225 points) 5 10 15
selected Jan 5, 2018 by sforrest072
 
Best answer

Magnitude of one of the magnetic fields, B1 = 1.2 × 10−2 T
Magnitude of the other magnetic field = B2
Angle between the two fields, θ = 60°
At stable equilibrium, the angle between the dipole and field B1, θ1 = 15°
Angle between the dipole and field B2, θ2 = θ − θ1 = 60° − 15° = 45°
At rotational equilibrium, the torques between both the fields must balance each other.
Torque due to field B1 = Torque due to field B2
MB1 sinθ1 = MB2 sinθ2
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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