d
Force on one pole

\(F = \frac{{m{\mu _0}I}}{{2\pi \sqrt {{d^2} + {x^2}} }}\)

\(m=\) pole strength

Total force \(=2 F \sin \theta\)

\(=\frac{2 \times \mu_{0} \operatorname{Im} \times x}{2 \pi \sqrt{d^{2}+a^{2}} \sqrt{d^{2}+a^{2}}}=\frac{\mu_{0} \operatorname{Im} x}{\pi\left[d^{2}+a^{2}\right]}\)

\(=m 2 x=M=I \pi a^{2}\)

Total force \(=\frac{\mu_{0} I a^{2}}{2\left(d^{2}+a^{2}\right)}\)

\(\approx \frac{\mu_{0} I a^{2}}{2 d^{2}} \quad[\because d>>a]\)