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Question -

A magnetic dipole is under theinfluence of two magnetic fields. The angle between the field directions is60º, and one of the fields has a magnitude of 1.2 × 10−2 T. Ifthe dipole comes to stable equilibrium at an angle of 15º with this field, whatis the magnitude of the other field?



Answer -

Magnitude of one of the magneticfields, B1 = 1.2 × 10−2 T

Magnitude of the other magneticfield = B2

Angle between the twofields, θ = 60°

At stable equilibrium, the anglebetween the dipole and field B1θ1 =15°

Angle between the dipole andfield B2θ2 = θ − θ=60° − 15° = 45°

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

Torque due to field B1 = Torque due tofield B2

MB1 sinθ1 = MB2 sinθ2

Where,

M =Magnetic moment of the dipole

Hence, the magnitude of the othermagnetic field is 4.39 × 10−3 T.

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