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Q.

A short bar magnet of length 1 cm has points A & B along its axis at distances of 24 cm and 48 cm on the opposite sides. Ratio of magnetic fields at these points will be:

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a

8

b

$\frac{1}{2 \sqrt{2}}$

c

3

d

4

answer is A.

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Detailed Solution

For a short magnet at a point along its axial line
$B = \frac{μ_{0}}{4 π} . \frac{2 M}{r^{3}}$
$∴ \frac{B_{A}}{B_{B}} = {(\frac{r_{2}}{r_{1}})}^{3} \Rightarrow \frac{B_{A}}{B_{B}} = {(\frac{48}{24})}^{3} = \frac{8}{1} = 8$
$∴ B_{A} : B_{B} = 8 : 1$

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