The magnetic field at the center of a circular coil is ul/2r.
It can be considered that the entire circular coil is divided into a large number of current elements, each of length dl. According to Biot-Savart law, the magnetic field dB at the centre O of the coil due to current element I ,dl is given by,
dB = u0 I (dl x r)/ 4πr^3
r is the position vector.
after solving we get that
dB = uIdlsinФ/4πr^2
and after solving again we get, since the turn of the coil is 1.
B = uI/2r
Hence the magnetic field at the center of a circular coil is ul/2r.
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