Question

A bar magnet of length $3\text{cm}$ has points $A$ and $B$ along its axis at distances of $24\text{cm}$ and $48\text{cm}$ from its centre on the opposite sides, the ratio of magnetic fields at the points will be

• A. $8$
• B. $\frac{1}{2\sqrt{2}}$
• C. $3$
• D. $4$

Answer 1

The correct option is A $8$

Magnetic field due to a bar magnet on its axial line is given by,

$\overrightarrow{B_a}=\frac{{\mu }_0}{4\pi }\frac{2\overrightarrow{M}}{r^3}$

$\therefore \left|\overrightarrow{B_a}\right|\propto \frac{1}{r^3}$


Using the diagram,

$\frac{B_A}{B_B}={\left(\frac{r_B}{r_A}\right)}^3$

$\Rightarrow \frac{B_A}{B_B}={\left(\frac{2r}{r}\right)}^3=\frac{8}{1}$

Hence, $\left(A\right)$ is the correct answer.