Question

Electrons (mass m, charge –e) are accelerated from rest through a potential difference V and are then deflected by a magnetic field that is perpendicular to their velocity. The radius of the resulting electron trajectory is:

Answer 1

`r=(1)/(B)\sqrt{(2Vm)/(e)}`

Step-by-step explanation:

Let m and e are the mass and charge of an electron. It is accelerated from rest through a potential difference V and are then deflected by a magnetic field that is perpendicular to their velocity. Let v is the velocity of the electron. It can be calculated as :

`(1)/(2)mv^2=eV`

`v=\sqrt{(2eV)/(m)}`

When the electron enters the magnetic field, the centripetal force is balanced by the magnetic force as :

`(mv^2)/(r)=evB`

`r=(mv)/(eB)`

or

`r=(1)/(B)\sqrt{(2Vm)/(e)}`

So, the radius of the resulting electron trajectory is
`(1)/(B)\sqrt{(2Vm)/(e)}`. Hence, this is the required solution.