Explanation

(b) Consider a point P located on the axial line of a short bar magnet of magnetic length 2l and strength m. Let us find B at a point P which is at a distance z from the center of magnet. Magnetic flux density at P due to N pole is
$B_{1} = \frac{\mu_{0}}{4\pi}\frac{m}{(z - l)^{2}\ }\ along\ NP$
Similarly, on S pole
$B_{2} = \frac{\mu_{0}}{4\pi}\frac{m}{(z + l)^{2}\ }\ along\ S$
Net magnetic flux at P is
$B = B_{1} - B_{2} = \frac{\mu_{0}}{4\pi}\left\lbrack \frac{m}{(z - l)^{2}} - \frac{m}{(z + l)^{2}} \right\rbrack\ $
$\ \ \ \ = \frac{\mu_{0}}{4\pi}\left\lbrack \frac{4mzl}{\left( z^{2} - l^{2} \right)^{2}} \right\rbrack$
$\ \ \ \ = \frac{\mu_{0}}{4\pi}\left\lbrack \frac{m \times 2l}{\left( z^{2} - l^{2} \right)^{2}}.2z \right\rbrack$
$\ \ \ \ = \frac{\mu_{0}}{4\pi}\left\lbrack \frac{2Mz}{\left( z^{2} - l^{2} \right)^{2}} \right\rbrack\ $
$B = \frac{\mu_{0}}{4\pi}\frac{2M}{z^{3}}\ \ \ \ \ \ \ \ \ (\because z > \ > l^{2})$