Question

A bar magnet of length $ 3 \,cm $ has points $ A $ and $ B $ along its axis at distances of $ 24\, cm $ and $ 48 \,cm $ on the opposite sides. Ratio of magnetic field at the opposite sides. Ratio of magnetic fields at these points will be

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

Answer 1

Answer: (A)

For a short magnet at a point along its axial line
$B=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{r^{3}}$
$\Rightarrow \frac{B_{1}}{B_{2}}=\left(\frac{r_{2}}{r_{1}}\right)^{3}=\left(\frac{48}{24}\right)^{3}=\frac{8}{1}=8$