Question

Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed 20 cms in tan A position from the compass needle. The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to(a) 20 cms(b) $20(2)^{1/3}$ cms(c) $20(2)^{2/3}$ cms(d) $20(2)^{3/3}$ cms

Answer 1

The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to

$20(2)^{1/3}$ cms

Answer 2

Given that,

Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed 20 cms in tan A position from the compass needle.

To find,

The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to what?

Solution,

Magnetic field intensity, $H=\dfrac{\mu_o}{\pi}\dfrac{2M}{d^3}$

No deflection position,

$\dfrac{\mu_o}{\pi}\dfrac{2M_1}{d_1^3}=\dfrac{\mu_o}{\pi}\dfrac{2M_2}{d_2^3}\\\\\dfrac{M_1}{M_2}=(\dfrac{r_1}{r_2})^3\\\\\dfrac{M_1}{2M_1}=(\dfrac{20}{r_2})^3\\\\r_2=20\times 2^{1/3}$

Hence, the correct option is (b).