Question

(i) Derive and expression for axial magnetic field of a bar magnet act as an equivalent solenoid.
(ii) A magnetized needle is a uniform magnetic field experience a torque but no net force. An ion nail near a bar magnet, however experience a force of attraction is addition to a torque. Why?

Answer 1

$\overrightarrow{B}$ at point $P$ is

Force expended by a unit north-south pole at $P$.

$=F_N-F_s$

$=\frac{N_{O}qm}{4x}(\frac{1}{(r-l{)}^2}-\frac{1}{(r+l{)}^2})$

$=\frac{N_{O}qm}{4x}\frac{4rl}{(r^2=l^2{)}^2}$

$qm\cdot 2l2m$ is magnetic dipole

$=\frac{N_O}{4x}\frac{2mr}{(r^2-l^2{)}^2}$

$l<<r$

$=\frac{{\mu }_0}{4x}\frac{2\overrightarrow{m}}{r^3}$