# Electron in a magnetic field

1. May 2, 2013

### Pranav-Arora

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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).

2. May 2, 2013

### technician

I agree with you ! I would say C and D are correct

3. May 2, 2013

### Pranav-Arora

Thanks technician for the check. :)

4. May 3, 2013

### judas_priest

Yup, it is C and D. Work done = evB.dScosθ
θ here, = 90. Hence it IS C and D.