Question

Two short magnets have the same pole strengths but one is twice as long as the other. The shorter one is placed at a distance of $0.2m$ from magnetometer, set in $\tan A$ position. The distance at which the other must be placed on the other side of the magnetometer so that there may be no deflection is :

$(2^{1/3}=1.26)$

• A. $0.252cm$
• B. $25.2cm$
• C. $12.5cm$
• D. $2.52cm$

Answer 1

The correct option is B $25.2cm$

The magnetic moment of the short magnet be '$M$' , the magnetic moment of the longer magnet will be '$2M$'
The deflection of the magnetic needle in $\tan A$ position by a short magnet is given by
$B_1=\frac{{\mu }_o}{4\pi }\frac{2M_A}{d_A^3}=B_H\tan {\theta }_A$

The deflection of the magnetic needle in $\tan B$ position by a long magnet is given by
$B_2=\frac{{\mu }_o}{4\pi }\frac{2M_B}{d_B^3}=B_H\tan {\theta }_B$
For the deflection to be zero , magnetic field due to both the magnets should be same.
$B_1=B_2\Rightarrow \frac{M_A}{d_A^3}=\frac{M_B}{d_B^3}$
But $M_A=M,M_B=2M$

$\frac{d_A^3}{d_B^3}=\frac{1}{2}$
$d_B=1.26\times 0.2=0.252m=25.2cm$