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Question
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 × 10–2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?
Solution
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 sin θ1 = MB2 sin θ2
Where,
M = Magnetic moment of the dipole
∴ B2 = `("B"_1 sin θ_1)/(sin θ_2)`
= `(1.2 xx 10^-2 xx sin 15°)/(sin 45°)`
= 4.39 × 10−3 T
Hence, the magnitude of the other magnetic field is 4.39 × 10−3 T.
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