In the figure, an electron accelerated from rest through potential difference V_

Question

In the figure, an electron accelerated from rest through potential difference V_1 = 1.38 kV enters the gap between two parallel plates having separation d = 22.3 mm and potential difference V_2= 54.9 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? Number Units

Explanation / Answer

KE of electron = qV

0.5mv^2 = qV

0.5*9.11*10^-31*v^2 = 1.6*10^-19*1380

v = 2.2*10^7 m/s

Electric feild between the plates of capacitor = V/d

= 59.4 / 0.0223 = 2663.67 V/m

Force between the plates of capactior due to electric and magnetic field will be the same

qE = qvB

B = E/v = 2663.67 / 2.2*10^7

= 1.2*10^-4 T

B = 0.112k mT

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