A magnetic dipole is under the influence of two magnetic fields. The angle between field directions is 60 degree on eof the fields has a magnitude of 1.2x10-2 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? (2M)
A magnetic dipole is under the influence of two magnetic fields. The angle between field directions is 60 degree on eof the fields has a magnitude of 1.2x10-2 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? (2M)
Magnitude of one of the magnetic fields, B 1 = 1.2 × 10 −2 T
Magnitude of the other magnetic field = B 2
Angle between the two fields, θ = 60°
At stable equilibrium, the angle between the dipole and field B 1 , θ 1 = 15°
Angle between the dipole and field B 2 , θ 2 = θ − θ 1 = 60° − 15° = 45°
At rotational equilibrium, the torques between both the fields must balance each other.
∴Torque due to field B 1 = Torque due to field B 2
MB 1 sin θ 1 = MB 2 sin θ 2
Where,
M = Magnetic moment of the dipole
Hence, the magnitude of the other magnetic field is 4.39 × 10 −3 T
Magnitude of one of the magnetic fields, B 1 = 1.2 × 10 −2 T
Magnitude of the other magnetic field = B 2
Angle between the two fields, θ = 60°
At stable equilibrium, the angle between the dipole and field B 1 , θ 1 = 15°
Angle between the dipole and field B 2 , θ 2 = θ − θ 1 = 60° − 15° = 45°
At rotational equilibrium, the torques between both the fields must balance each other.
∴Torque due to field B 1 = Torque due to field B 2
MB 1 sin θ 1 = MB 2 sin θ 2
Where,
M = Magnetic moment of the dipole
Hence, the magnitude of the other magnetic field is 4.39 × 10 −3 T
