Change in orbital magnetic dipole moment of the electron due to unifrom B field

[dlslhc]

Homework Statement

Assume that an electron of mass m and charge magnitude e moves in a circular orbit of radius r about a nucleus. A uniform magnetic field B is then established perpendicular to the plane of the orbit. Assuming also that the radius of the orbit does not change and that the change in the speed of the electron due to field B is small, find an expression for the change in the orbital magnetic dipole moment of the electron due to the field.

Homework Equations

F = qvB = mv²/r => v = eBr/m
μ = evr/2

The Attempt at a Solution

i calculated μ = e²Br²/2m
but the answer from textbook is e²Br²/4m , where is the 2 come from or the text is wrong? thank you

 

[anathema]

Hello,

Thank you for your question. Your attempt at the solution is correct. The expression for the orbital magnetic dipole moment of an electron due to a perpendicular magnetic field is indeed μ = e2Br2/2m. The textbook answer is most likely a typo. The 2 in the denominator should not be there. It is also possible that the textbook is using a different set of units, in which case the expression would be different. However, assuming that both you and the textbook are using SI units, your answer is correct.

I hope this helps. Let me know if you have any further questions.

 

[kerimek]

Thank you for your question. It appears that the textbook may have a typo or error in their solution. In your solution, you have correctly calculated the orbital magnetic dipole moment of the electron due to the uniform magnetic field. The textbook's answer of e2Br2/4m is incorrect as it does not take into account the correct expression for the velocity of the electron in a circular orbit, which is v = eBr/m. Your solution of e2Br2/2m is the correct expression for the change in the orbital magnetic dipole moment of the electron due to the uniform magnetic field.