At two points separated by a distance of $3 c m$ , the magnetic field strength due to a short magnet on its axial line are in the ratio $512 : 125$ . Then the distance of magnet from the first point is:

8 c m

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11 c m

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4 c m

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5 c m

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Solution

The correct option is C $5 c m$

$d_{1} = d$
$d_{2} = (d + 3)$
$\frac{B_{1}}{B_{1}} = \frac{512}{125}$
$B = \frac{μ_{0} m}{4 π d^{3}}$
$= \frac{512}{125}$
${(\frac{d_{2}}{d_{1}})}^{3} = \frac{512}{125}$
$\frac{d_{2}}{d_{1}} = \frac{8}{5}$
$\frac{d + 3}{d} = \frac{8}{5}$
$d = 5$ cm

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