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  4. Two uniform magnetic fields B and H are perpendicular to each other. At a place when a magnetic needle is placed in the field, it rest making angle of 60° and 30° with B and H respectively. The value of B: H is:

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Q. Two uniform magnetic fields $B$ and $H$ are perpendicular to each other. At a place when a magnetic needle is placed in the field, it rest making angle of $60^{\circ}$ and $30^{\circ}$ with $B$ and $H$ respectively. The value of $B : H$ is:

Magnetism and Matter

Solution:

$B=B_{0} \cos 60^{\circ}$
$H=B_{0} \cos 30^{\circ}$
$\frac{B}{H}=\frac{\cos 60^{\circ}}{\cos 30^{\circ}}$
$=\frac{1 / 2}{\sqrt{3} / 2}=\frac{1}{\sqrt{3}}$