An electron accelerated from rest through potential as shown

An electron accelerated from rest through potential as shown the gap between two plates having separation d=20.0mm and also ignoring graviltaonal force. determine the required uniform magnetic field between two . direction) that allows the electron to travel In a straight line give your reasoning for the direction of magnetic field determined

Solution

kinetic energy gained by he electron when it is accelerated = work done by the potential differnce on it
= e*1.0 kV = 1.6*(10^-16)
where e is the magnitude of charge on the electron.

so, (1/2)m*(v*v) = 1.6*(10^-16)
=> v = 1.87* (10^7)
Now, between the plates, potential difference = 100 V
separation = 20.0 mm = 0.02 m
So, electric field between the plates = V/d = 100/0.02
= 5000 N/C

Now, the magnetic field is applied perpendicular to the velocity of the electron, let its magnitude be B.

Then, magnetic force on the electron = e*v*B = electric force = e*5000
So, B= 5000/v = 2.67*(10 raise to power -4) Tesla.