An electron is accelerated through a potential difference of 3.1 kV and directed into a region between two parallel plates separated by 17 mm with a potential difference of 100 V between them. The electron is moving perpendicular to the electric field when it enters the region between the plates. What magnetic field is necessary perpendicular to both the electron path and the electric field so that the electron travels in a straight line?

Answer: 178.25*10^-6 T

Explanation: In order to solve this problem we have to take into account the equilibrium between the electric and magnetic forces in the electron, so it is given by:

Fm=evB

Fe=eE so

evB=eE the we have

v=E/B

Firsly we calculate the velocity of the electron before to get the parallel plates at 100V

eΔV=1/2*m*v^2 then

v = (2*eΔV/m) ^1/2

v = (2*1.6*10^-19*3.1*10^3/9.1*10^-31) ^1/2=33 * 10^6 m/s

Then we can calculate B

B=E/v E. d=V where d is the separation between the plates and V is equal a 100V

B=V / (d*v) = 100 / (17*10^-3*33 * 10^6) = 178.25*10^-6 T