5.21 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?

 

 
 
Magnitude of one of the magnetic field, B1=1.2×10-2T
Magnitude of the other magnetic field, B2
Angle between the two fields, θ=60°
At stable equilibrium, the angle between the dipole and field B1θ1=15°
Angle between the dipole and field B2,θ2=θ-θ1=60°-15°=45°
|At rotational equilibrium, the torques between both the field
must balance each other.
 
 
TorqueduetofieldB1=TorqueduetofieldB2
MB1sinθ1=MB2sinθ2
Where,
M=Magneticmomentofhtedipole
B2=B1sinθ1sinθ2=1.2×102×sin15sin45=4.39×103T
Hence, the maanituda if tha otharmaanatic fiale is 4.39×10-3T.