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Deduce an expression for the magnetic di...

Deduce an expression for the magnetic dipole moment of an electron orbiting around the central nucleus.

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Consider an electron revolving in a circular orbit of radius r with speed v and frequency v. If the electron cross a point P on the circle in every revolution, then distance travelled by electron to complete on revolution `=2pi r.`
No. of revolutions in one second `(v)=(v)/(2pi r)`
The electric current `(i) =("charge")/("time")="charge " xx "frequency"`
`i=exx(v)/(2pi r)`
`therefore` Magnetic dipole moment (M) = iA `" "(because N=1)`
`M=(ev)/(2pi r)xxpir^(2)" "(because A= pi r^(2)`
`M=(evr)/(2)`
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