Please show all work so I get a good explanation. Thank you! An electron acceler

Question

Please show all work so I get a good explanation. Thank you!

An electron accelerated from rest through potential difference V1 = 1.14 kV enters the gap between two parallel plates having separation d = 19.6 mm and potential difference V2 = 100 V. The lower plate is at the lower potential. Neglect fringing and assume that the election'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

workdone on electron, W = q*V

w = 1140*1.6*10^-19

W = 1.824*10^-16 J

we know, W = 0.5*m*v^2

==> v = sqrt(2*W/m)

= sqrt(2*1.824*10^-16/9.1*10^-31)

= 2.002*10^7 m/s

Electric filed between paltes, E = V2/d = 100/0.0196 = 5102 N/c

when net force equal to zero the lectron moves in a stright line.

so, FB = Fe

q*v*B = q*E

==> B = E/v = 5102/2.002*10^7 = 2.55*10^-4 T <<<<<----Answer


here the direction of magnetic filed should be in to the the page.

so, Bx = 0

By = 0

Bz = -2.55*10^-4 T

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