Two bar magnets with area $a$, in axis, at a distance of $d$ ($d$ is much biffer than $a$) attract each other with a force of $F$.
What is the force between two infinite surfaces made of the same material, at the distance of $d$ per $a$?

My work:

According to Wikipedia in those circumstances the force between the surfaces is calculated by:

$F = \frac{B^2A}{2μ}$

The only variable I'm missing is B.
Now, the force between two poles is:

$F = \frac{μq_1q_2}{4πd^2}$

Sadly I have no idea how to use the calculated $q_1\cdot q_2$ to get $B$.

What is the missing step?


That is a much complex approach to solving the problem. What I instead suggest is to consider the magnetic strength ($q_m$) which is the charge the hypothetical monopole would have. Considering it as an electrostatic system solve it using the equations of electrostatics by replacing 1/$\epsilon_0$ by $\mu_0$.

B is nothing but an analogue to E for a dipole ($q_m$ and $-q_m$).


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