Derive an expression for the magnetic field \(B\), due to a circular coil of \(N\) turns, each of radius \(r\) carrying current \(I\), at a distance \(x\) from the centre along its axis.
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At the center of the loop (\(x=0\)):
\[
B = \frac{\mu_0 N I}{2r}
\]
Always use symmetry to avoid full integration.