Q. A short bar magnet has a length $2l\ $ and a magnetic moment$\ 10\ Am^{2}$. 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) $2 \times 10^{- 3}\ T$
B) $3 \times 10^{- 3}\ T$
C) $1 \times 10^{- 3}\ T$
D) $4 \times 10^{- 3}\ T$
Explanation
(a) On axial position
$B_{a} = \frac{\mu_{0}}{4\pi}\frac{2Mr}{\left( r^{2} - l^{2} \right)^{2}};if\ l < \ < r,\ then\ B_{a} = \frac{\mu_{0}}{4\pi}\frac{2M}{r^{3}}$
$B_{a} = \frac{10^{- 7}\ \times \ 2\ \times \ 10}{(0.1)^{3}} = 2 \times 10^{- 3}\ T\ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack\because z = r\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.