Physics, asked by Rohan9224, 1 year ago

Obtain an expression for the magnetic moment of an electron moving with a speed ‘v’ in a circular orbit of radius ‘r’. How does this magnetic moment change when : 4 (i) the frequency of revolution is doubled? (is) the orbital radius is halved?

Answers

Answered by sidd15
2

Magnetic moment arises in revolving electron because of its intrinsic property of called spin.



A revolving electron is equivalent to a current loop; the equivalent current being

where T = time period
If r = radius of loop and v the speed of electron, then

Angular momentum of revolving electron,

where

mass of electron.
Dividing (4) by (5), we get

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OTHER ANSWERS

Souradeep Roy Choudhury, Dual degree Engineering Physics, Indian Institute of Space Science & Technology (2020)
Answered Nov 2 2017 · Author has 117 answers and 19.4k answer views
Thanks for the A2A.

For a revolving electron which carries a charge e(equal to electronic charge) , spinning around the nucleus with a radius equal to bohr radius a0, the current flowing is equal to eT=ev2πr,eT=ev2πr, where v is the velocity of the electron.

Hence, magnetic moment= Current*Area=ev2πr(πr2)=evr2ev2πr(πr2)=evr2.

Now, for calculating v, Centripetal force= Electrostatic force.

Hence,mv2r=KZe2r2.mv2r=KZe2r2.

Also, one has the orbital momentum quantization: mvr=nh2πmvr=nh2π.

Hence, finally substitute r and v in terms of n and other known constants.

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Sangam Singh, Avid reader
Answered Jun 4 2014
Magnetic Dipole Moment of a Revolving Electron

An atom consists of positively charged heavy nucleus around which negatively
charged electrons are revolving in circular orbit.



The electron of charge (-e) performs U.C.M. (uniform circular motion) around a stationary nucleus with
period of revolution T. If r be the radius of the orbit of revolution of the electron
and v is the orbital velocity then


Magnitude of magnetic moment associated with circular current is

The direction of this magnetic moment is into the plane of paper. Negatively
charged electron is moving in anticlockwise direction, leading to a
clockwise current.
Multiplying and dividing the right hand side of equation (5) by the mass of
electron, me then

The negative sign indicates that the orbital angular momentum of
electron is opposite in the direction to the orbital magnetic moment.

The ratio of magnetic dipole moment with angular momentum of
revolving electron is called the gyromagnetic ratio.

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