#### 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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#### APPEARS IN

Solution Show that the Orbital Magnetic Dipole Moment of a Revolving Electron Is (eVr)/2 Concept: Magnetic Dipole Moment of a Revolving Electron.