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(C) Let the length of the magnet be $2l = 2 \ cm$,so $l = 1 \ cm$.The distance of point $A$ from the center of the magnet is $r_1 = x + l = x + 1$.The

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$8 : 1$ approximately

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(C) Let the length of the magnet be $2l = 2 \ cm$,so $l = 1 \ cm$.The distance of point $A$ from the center of the magnet is $r_1 = x + l = x + 1$.The distance of point $B$ from the center of the magnet is $r_2 = 2x + l = 2x + 1$.For a short magnet or points at large distances,the magnetic field $B \propto \frac{1}{r^3}$.Thus,the ratio of the magnetic fields is $\frac{B_A}{B_B} = \left( \frac{r_2}{r_1} \right)^3 = \left( \frac{2x + 1}{x + 1} \right)^3$.If $x \gg l$,then $\frac{B_A}{B_B} \approx \left( \frac{2x}{x} \right)^3 = 2^3 = 8$.Therefore,the ratio is $8 : 1$ approximately.

Two points $A$ and $B$ are situated at a distance $x$ and $2x$ respectively from the nearer pole of a magnet $2 \ cm$ long. The ratio of the magnetic field at $A$ and $B$ is

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