If wire of length $L$ form a loop of radius $R$ and have $n$ turn. Find magnetic field at centre of loop if current flowing in loop is $I$
Diffcult
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$\mathrm{L}=\mathrm{n}[2 \pi \mathrm{R}] \Rightarrow \mathrm{R}=\frac{\mathrm{L}}{2 \pi \mathrm{n}}$
$B=n\left[\frac{\mu_{0} i}{2 R}\right]=n\left[\frac{\mu_{0} i}{2 \frac{L}{2 \pi n}}\right]$
$B=n\left[\frac{\mu_{0} i}{2 L} \times 2 \pi n\right]$
$=\frac{\mu_{0} i}{2 L \times 2 \pi} \times 2 \pi n^{2} \times 2 \pi$
$B=\frac{\mu_{0} i}{4 \pi} \frac{4 \pi^{2} n^{2}}{L}$
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