How to calculate magnetic induction just beyond the end of the magnet?

[Lotto]

Homework Statement

Calculate magnetic induction just beyond the end of a bar magnet on its axis

Relevant Equations

$$B=\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2},$$ where r → l.

I know I should use a limit $$B=\lim_{r\to l}{\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2}},$$,but in Wolfram I get a weird solution. https://www.wolframalpha.com/input?i2d=true&i=Limit[Divide[4rl,Power[\(40)Power[r,2]-Power[l,2]\(41),2]],r->l]

What is the solution? It shouldn't be infinity.

 

[kuruman]

Homework Statement:: Calculate magnetic induction just beyond the end of a bar magnet on its axis
Relevant Equations:: $$B=\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2},$$ where r → l.

I know I should use a limit $$B=\lim_{r\to l}{\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2}},$$,but in Wolfram I get a weird solution. https://www.wolframalpha.com/input?i2d=true&i=Limit[Divide[4rl,Power[\(40)Power[r,2]-Power[l,2]\(41),2]],r->l]

What is the solution? It shouldn't be infinity.

According to the expression you quoted, it should be infinity. Note that you are asked to find the magnetic induction just beyond the end of the magnet, not at the end of the magnet. Also, I think your expression was derived in the limit $r>>l$ so you can't do much with it when $r\approx l$. You need to go back to the original expression from which your equation was derived and see what you get when you substitute $r=l+\epsilon$ with $\epsilon/l <<1$.