# Magnetic induction in solenoid

I found an equation in theory about magnetic induction in a solenoid: $B_s=\mu_0 I n$. It should be magnetic induction for infinite length solenoid. I wonder if this is anyhow useful. Where can this be used?

($n = \frac {N}{L}$, where $L$ is length of solenoid and $N$ is number of turns... which doesn't make sense to me, if the length is supposed to be infinite)

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Then field inside at a point comes out to be $$\dfrac12 \mu_0nI\bigg[\dfrac{b}{\sqrt{b^2+r^2}}+\dfrac{a}{\sqrt{a^2+r^2}}\bigg]$$ where $a$ and $b$ are distances from the point to the ends of solenoid.
We can see if $r<<a,b$ then field comes out to be$$\mu_0nI$$ and this condition is called infinite length.
In our materials it is $$\dfrac12 \mu_0nI\bigg[\dfrac{b}{\sqrt{b^2+r^2}}-\dfrac{a}{\sqrt{a^2+r^2}}\bigg]$$ and that would be $0$. If I put here $+$, graph is not right. – user50222 Apr 20 '13 at 14:27
@user23125 It must be in vector form or in other words the a,b are taken with directions.I have given the magnitude and direction has to be seen physically. So, in your case , if you see $\vec a$ would be negetive and so magnitude will come out to be $\mu_0nI$ – ABC Apr 20 '13 at 14:33