A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle, of 75∘. One of the fields has a magnitude of √2×10−2T. The dipole attains stable equilibrium at an angle of 30∘ with this field. What is the magnitude of the other field?
0.01 T
Refer to Fig. Let θ1 (=30∘) be the angle between the magnetic moment vector m and the field vector B1(=1.5×10−2T). Then, as shown in Fig. the angle between m and the other field B2 will be θ2=75∘−30∘=45∘
The field B1 exerts a torque τ1=m×B1 on the dipole and the field B2 exerts a torque τ2=m×B2, where m in the magnetic moment of the dipole. Since the dipole is in stable equilibrium, the net torque τ(=τ1+τ2) must be zero, i.e. the two torques must be equal and opposite. In terms of magnitudes, we have mB1 sin θ1=mB2 sin θ2
or B2=B1 sin θ1sin θ2=√2×10−2×sin 30∘sin 45∘=0.01 T