Magnetic moment of revolving electron derivation 2th
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charge constitutes current. Same can be said about an electron revolving around a nucleus

For an electron of charge e revolving around a nucleus of charge Ze at an orbit of radius r, with velocity vmagnetic moment μl is calculated by the following method:
First, we will find the current i due to electron revolution:
i = e/T
T = 2πr/v
∴i = ev/(2πr)
Now, we know that magnetic moment μlis given by:
μl = iA= iπr2
μl = ev/(2πr) × πr2 = evr/2
On multiplying and dividing by mass of electron me, we get :
μl = emevr/(2me)
Here, mevr = L (angular momentum of electron, perpendicular to the plane of paper outwards)
∴μl = -eL/(2me)
Where, minus sign signifies that angular momentum’s direction is opposite to the magnetic moment’s direction.

For an electron of charge e revolving around a nucleus of charge Ze at an orbit of radius r, with velocity vmagnetic moment μl is calculated by the following method:
First, we will find the current i due to electron revolution:
i = e/T
T = 2πr/v
∴i = ev/(2πr)
Now, we know that magnetic moment μlis given by:
μl = iA= iπr2
μl = ev/(2πr) × πr2 = evr/2
On multiplying and dividing by mass of electron me, we get :
μl = emevr/(2me)
Here, mevr = L (angular momentum of electron, perpendicular to the plane of paper outwards)
∴μl = -eL/(2me)
Where, minus sign signifies that angular momentum’s direction is opposite to the magnetic moment’s direction.
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