Question

A short bar magnet has a length $2l$ and a magnetic moment $10 \, A \, m^{2}$ . Find the magnetic field at a distance of $z=0.1 \, m$ from its centre on the axial line. Here, $l$ is negligible as compared to $z$ .

• A. $4\times 10^{- 3} \, T$
• B. $1\times 10^{- 3} \, T$
• C. $3\times 10^{- 3} \, T$
• D. $2\times 10^{- 3} \, T$

Answer 1

Answer: (D)

If the point lies on the axial line of bar magnet
$B=\frac{\mu . \, 2 M d}{4 \pi \left(d^{2} - l^{2}\right)^{2}}$
If $l < \, < d$ (as given in the question)
$B=\frac{\mu _{0}}{4 \pi }\times \frac{2 M}{d^{3}}$
$=\frac{\mu _{0}}{4 \pi }\times 20\times 10^{3}$
$\left(\frac{\left(\mu \right)_{0}}{4 \pi } = \left(10\right)^{- 7}\right)$
$=2\times 10^{- 3} \, T$