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  4. A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75o . One of the fields has a magnitude of 15 mT . The dipole attains stable equilibrium at an angle of 30o with this field. The magnitude of the other field (in mT ) is close to

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Q. A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of $75^{o}$ . One of the fields has a magnitude of $15 \, mT$ . The dipole attains stable equilibrium at an angle of $30^{o}$ with this field. The magnitude of the other field (in $mT$ ) is close to

NTA AbhyasNTA Abhyas 2022

Solution:

$\theta _{1} + \theta = 75^{o}$
$MB_{1}\sin\theta _{1}=MB_{2}\sin\theta $
$\Rightarrow \frac{B_{1}}{\sqrt{2}}=\frac{15}{2}$
$\Rightarrow B_{1}=\frac{15}{\sqrt{2}}\approx11 \, mT$