Question

Show that time period of revolution an electron beam in uniform magnetic field is independent of velocity and radius of path

Answer 1

Since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path

How to show that time period of revolution an electron beam in uniform magnetic field is independent of velocity and radius of path?

For an electron moving in a uniform magnetic field, the force on the electron is given by

F = Bev where

• B = magnetic field,
• e = electron charge and
• v = speed of electron

Also, this magnetic force equals the centripetal force on the electron, F'

F' = mv²/r where

• m = mass of electron,
• v = speed of electron and
• r = radius of path

Since both forces are equal,

F = F'

Bev = mv²/r

Be = mv/r

We know that angular speed, ω = v/r. So,

Be = mω

Also, angular speed, ω = 2π/T where T = period of revolution of electron

So, Be = m2π/T

Making T subject of the formula, we have

T = 2πm/Be

so, since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path

Learn more about period of revolution of electron here:

https://brainly.com/question/17081554

#SPJ1