In the figure an electron accelerated from rest theough Negl

In the figure, an electron accelerated from rest theough Neglect fringing and assume that the electron\'s velocity vectar is perpendticudar to the lacaie potential ditterence 1.7 kv enters the g vectar is perpendicular to the electric field vector betwen the plates what uiderm agnatic fels allows the electron to travel gap between two parallel plates having separation 20.0 mm and pates having separaion 20.0 mm and petential dfference 200 V. The lower plate is at the lower poteatial. in a straight ine in the gap? Cross product Unit Vector Notation

Solution

For the electron to travel in a straight line, the net force must be zero. This means that the electric force equals the magnetic force

F = qE = qvB

B = E/v

1. V2 = E*d

E = V2/d = 200/20*10^-3 = 10000 V/m

2. KE = 0.5*mv^2 = qV1

v = sqrt(2qV1/m) = sqrt(2*1.6*10^-19*1.7*10^3/(9.1*10^-31)) = 2.45*10^7 m/sec

which gives

B = E/v = 10000/(2.45*10^7) = 4.08*10^-4 T