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Question
Show that the orbital magnetic dipole moment of a revolving electron is `("evr")/2`
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Solution
Expression for magnetic dipole moment:
- Consider an electron of mass me and charge e revolving in a circular orbit of radius r around the positive nucleus in the clockwise direction, leading to an anticlockwise current.
U.C.M of an electron around the nucleus - If the electron travels a distance 2πr in time T then, its orbital speed v = 2πr/T
- The magnitude of circulating current is given by, I = e`(1/"T")`
But, T = `(2pir)/"v"`
∴ I = e`(1/(2pir"/""v")) = ("ev")/(2pir)` - The orbital magnetic moment associated with the orbital current loop is given by,
morb = IA = `("ev")/(2pir) xx pi"r"^2` .....….[∵ Area of current loop, A = πr2]
∴ morb = `"evr"/2`
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