Electron in a magnetic field statements

AI Thread Summary
In a discussion about the behavior of electrons in a magnetic field, it was established that the work done on electrons by the magnetic field is zero, confirming statement D as correct. Since no work is done, energy gained is also zero, eliminating statement A. The radius of the electron's path was derived as p/(eB), validating statement C. However, the centripetal force equation led to a misunderstanding regarding statement B, which was found to be incorrect. Ultimately, the consensus is that statements C and D are true, despite the answer key only acknowledging C.
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Homework Statement


A beam of electrons moving with a momentum p enters a uniform magnetic field of flux density B perpendicular to its motion. Which of the following statement(s) is (are) true?

A)Energy gained is ##p^2/2m##
B)Centripetal force on the electron is ##Bem/p##
C)Radius of the electron's path is ##p/(Be)##
D)Work done on the electrons by the magnetic field is zero.

Homework Equations


The Attempt at a Solution


The force due to magnetic field on an electron is always perpendicular to the motion and hence does no work on it. So D) is correct. Since no work is done, no energy is gained and A) is eliminated.

\because \frac{mv^2}{r}=evB \Rightarrow r=\frac{mv}{eB}=\frac{p}{eB}
where r is the radius of electron's path and hence C) is correct. From the above equation, mv^2/r represents the centripetal force. It is equal to eBp/m and B) also eliminates. Therefore, the statements which are true are C) and D) but the answer key states that it is C). :confused:
 
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I agree with you ! I would say C and D are correct
 
technician said:
I agree with you ! I would say C and D are correct

Thanks technician for the check. :)
 
Yup, it is C and D. Work done = evB.dScosθ
θ here, = 90. Hence it IS C and D.
 
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