What is the magnetic field induction at the centre of line joining the two poles of a horse shoe magnet of poles strength ‘m’ and separated by a distance ‘a’ is

The resultant magnetic field at the center of the magnet is 

                               $$\begin{gathered} B_R=B_N+B_S \\ But , B_N=B_S=\left(\frac{{\mu }_0}{4\pi }\frac{m}{r^2}\right) = \left(\frac{{\mu }_0}{4\pi }\frac{m}{{\left({\displaystyle \frac{a}{2}}\right)}^2}\right) = 4\left(\frac{{\mu }_0}{4\pi }\frac{m}{a^2}\right) \\ \therefore B_R= 4\left(\frac{{\mu }_0}{4\pi }\frac{m}{a^2}\right)+ 4\left(\frac{{\mu }_0}{4\pi }\frac{m}{a^2}\right) \\ \Rightarrow B_R=8\left(\frac{{\mu }_0}{4\pi }\frac{m}{a^2}\right) \end{gathered}$$