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?

Options

A. Energy gained by electrons in megnetic field 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

Answer

C, D

Explanation

`p=mv implies v=(p//m)`
Centripetal force=magnetic force `=evB=(ep)/(m)B`
Now `evB=(mv^(2))/(r) implies r=(mv)/(eB)=(p)/(eB)`
No work is done by magnetic field, so no energy is gained by eletrons in magnetic field.