In the figure below, an electron accelerated from rest through potential differe
ID: 2059422 • Letter: I
Question
In the figure below, an electron accelerated from rest through potential difference V1=1.39 kV enters the gap between two parallel plates having separation d = 16.8 mm and potential difference V2= 93.2 V. The lower plate is at the lower potential.Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates.
In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?
In the figure below, an electron accelerated from rest through potential difference V1=1.39 kV enters the gap between two parallel plates having separation d = 16.8 mm and potential difference V2= 93.2 V. The lower plate is at the lower potential.Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?Explanation / Answer
kinetic energy of electron,K =q*V1 = 1.60x10^-19 * 1390 = 2.224 x 10^-16 Joules
also,
K = (1/2) m v^2
2.224 x 10^-16 = (1/2) * 9.11 x 10^-31 v^2
v = 2.21*10^7 m/s
electric field E = V/d = 93.2/0.0168 = 5548 V/m
force on the electron,F = Eq directed towards upper plate
so, force due to magnetic field must be towards the lower plate directed downwards.
so, Fb = qvB and this must be equal to F
so, qvB = Eq
so, B = E/v = 2.51*10^-4 T
and this can be represented in vector notation as (+2.51*10^-4 k) Tesla