A magnetic dipole is under the influence of two magnetic fields. The angle between the two field direction is 750 and one of the fields has a magnitude of 52×10−3T. If the dipole comes to stable equilibrium at an angle of 300 with this field. The magnitude of the other field in (mT) is

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A magnetic dipole is under the influence of two magnetic fields. The angle between the two field direction is $75^{0}$ and one of the fields has a magnitude of $5 \sqrt{2} \times 10^{- 3} T .$ If the dipole comes to stable equilibrium at an angle of $30^{0}$ with this field. The magnitude of the other field in (mT) is

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Detailed Solution

As the dipole is in equilibrium the torque on the dipole due to the two fields are equal and opposite. If M is the magnetic dipole moment of the dipole, then

$\begin{matrix} ∴ M B_{1} \sin θ_{1} = M B_{2} \sin θ_{2} \\ \Rightarrow B_{2} = \frac{B_{1} \sin θ_{1}}{\sin θ_{2}} \end{matrix}$

$B_{2} = \frac{5 \sqrt{2} \times 10^{- 3} \times \frac{1}{2}}{\frac{1}{\sqrt{2}}} = 5 \times 10^{- 3} T$

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