The magnetic ...

Question

The magnetic field at a point $x$ on the axis of a small bar magnet is equal to the field at a point $y$ on the equator of the same magnet. The ratio of the distance of $x$ and $y$ from the centre of the magnet is?

2^{- 3}

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2^{- 1 / 3}

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2^{3}

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2^{1 / 3}

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Solution

The correct option is D $2^{1 / 3}$
As we know that,
On the axis, $B_{1} = \frac{2 M}{x^{3}}$ On the equator, $B_{2} = \frac{M}{y^{3}}$

as $B_{1} = B_{2}$

$\frac{2 M}{x^{3}} = \frac{M}{y^{3}}$

∴ $(\frac{x}{y})^{3} = 2$

$\frac{x}{y} = 2^{(1 / 3)}$

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As we know that,
On the axis, $B_{1} = \frac{2 M}{x^{3}}$ On the equator, $B_{2} = \frac{M}{y^{3}}$

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