Question

Points $A$ and $B$ are situated perpendicular to the axis of a $2cm$ long bar magnet at large distances $X$ and $3X$ from its centre on opposite sides. The ratio of the magnetic fields at $A$ and $B$ will be approximately equal to

• A. $1:9$
• B. $2:9$
• C. $27:1$
• D. $9:1$

Answer 1

The correct option is C $27:1$

Magnetic field at the axial of bar magnet is given by the relation as :

$B=\frac{{\mu }_O}{2\pi }\frac{M}{d^3}$

where d is the distance

So,

$B\propto \frac{1}{d^3}$

$\frac{B_A}{B_B}=\frac{{d_B}^3}{{d_A}^3}$

$\frac{B_A}{B_B}=\frac{27}{1}$

Hence, the ratio of magnetic field of $A$ and $B$ is $27:1$ .