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If an electron revolves around a nucleus in a
circular orbit of radius R with frequency n. then the
magnetic field produced at the center of the
nucleus will be

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The electron completes ‘n’ rounds per second, which means

frequency = n

Therefore, T=1n(AsT=1f)T=1n(AsT=1f)

As I=qTI=qT

Charge of an electron; q=e(e=1.6×1019)q=e(e=1.6×10−19)

I=e1/nI=e1/n

i.e, I = n×e

Magnetic field at a point P on the central axis of a circular loop which is at a distance ‘x' from the centre of the circular loop of radius 'R' is given by

B=μ0×I×r22×(x2+r2)32B=μ0×I×r22×(x2+r2)32

As x=0 (because the question asks for magnetic field at the center of the loop)

B=μ0×I2×rB=μ0×I2×r

we get;B=μ0×n×e2×r

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