Question

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

• A. $4:1$ exactly
• B. $4:1$ approximately
• C. $8:1$ exactly
• D. $8:1$ approximately

Answer 1

The correct option is D $8:1$ approximately

For a magnet $B=\frac{{\mu }_0}{4\pi }\frac{2M}{r^3}$(nearly)
$\Rightarrow \frac{B_2}{B_1}={\left(\frac{r_1}{r_2}\right)}^3$
$\Rightarrow \frac{B_2}{B_1}={\left(\frac{x}{2x}\right)}^3\Rightarrow \frac{B_2}{B_1}=\frac{1}{8}$.
Thus, $B_1:B_2=8:1$ approximately.