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

Answer:

$r=\dfrac{1}{B}\sqrt{\dfrac{2Vm}{e}}$

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 :

$\dfrac{1}{2}mv^2=eV$

$v=\sqrt{\dfrac{2eV}{m}}$

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

$\dfrac{mv^2}{r}=evB$

$r=\dfrac{mv}{eB}$

or

$r=\dfrac{1}{B}\sqrt{\dfrac{2Vm}{e}}$

So, the radius of the resulting electron trajectory is $\dfrac{1}{B}\sqrt{\dfrac{2Vm}{e}}$. Hence, this is the required solution.