Question

A bar magnet of length $3\text{cm}$ has point $A$ and $B$ along its axis at distance of $24\text{cm}$ and $48\text{cm}$ on the opposite sides, as shown in the diagram. Ratio of magnetic fields at these points will be,

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

Answer 1

The correct option is A $8$

Both $A$ and $B$ are axial points.

The magnetic field at an axial point is,

$\left|B\right|=\frac{2KM}{r^3}\Rightarrow \left|B\right|\propto \frac{1}{r^3}$

$\therefore \frac{\left|B_A\right|}{\left|B_B\right|}=\frac{{\left|r_B\right|}^3}{{\left|r_A\right|}^3}={\left(\frac{48}{24}\right)}^3=2^3=8$

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