Ncert Exercises & Solutions

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,

B_{1} = 1.2 \times 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 field
must balance each other.

∴ Torque due to field B_{1} = Torque due to field B_{2}

{MB}_{1} {sinθ}_{1} = {MB}_{2} {sinθ}_{2}

Where,

M = Magnetic moment of hte dipole

\begin{aligned} ∴ B_{2} & = \frac{B_{1} \sin θ_{1}}{\sin θ_{2}} \\ = \frac{1.2 \times 10^{- 2} \times \sin 15^{\circ}}{\sin 45^{\circ}} = 4.39 \times 10^{- 3} T \end{aligned}

Hence, the maanituda if tha otharmaanatic fiale is

4.39 \times 10^{- 3} T .

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