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Question
Show that the orbital magnetic dipole moment of a revolving electron is `(eVr)/2`
Solution
In an atom, electron revolves around the nucleus in circular motion. ‘e’ be the charge on electron. The T be the time required to complete one revolution.
`:."Period of revolution"="Circumference"/"velocity" " ":.T=(2pir)/v`
Circulating current `I=e/T" ":.I=(ev)/(2pir)`
Magnetic moment associated with electron circular loop = M = IA `:.M=(ev)/(2pir)xxpir^2`
`:.M=(evr)/2`
The direction of this magnetic moment is in to the plane of paper. Negatively charge electron is moving in anticlockwise direction leading current in clockwise direction.
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