In the figure, an electron accelerated from rest through potential difference 2.

Question

In the figure, an electron accelerated from rest through potential difference 2.4 kV enters the gap between two parallel plates having separation 20.0 mm and potential difference 180 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. What uniform magnetic field allows the electron to travel in a straight line in the gap?

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In the figure, an electron accelerated from rest through potential difference 2.4 kV enters the gap between two parallel plates having separation 20.0 mm and potential difference 180 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. What uniform magnetic field allows the electron to travel in a straight line in the gap?

Explanation / Answer

0.5*me*v^2 = 2.4*10^3 e volts

0.5*me*v^2 = 2.4*10^3*1.6*10^-19

v = sqrt(2*2.4*10^3*1.6*10^-19/9.1*10^-31)

v = 2.9*10^7 m/s



Fe = FB

q*E = q*v*B

V/d = v*B

==> B = V/(v*d) = 180/(2.9*10^7*20*10^-3) = 3.1*10^-4 T

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