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An electron enters the region between two horizontal parallel plates…
Question
An electron enters the region between two horizontal parallel plates moving horizontally with speed 2 x 10^7 m/s, parallel to and midway between the plates. The plates have length 0.04 m (along the motion) and separation 0.04 m, and a potential difference of 50 V is maintained across them. Taking electron charge 1.6 x 10^-19 C and mass 9.1 x 10^-31 kg, find the vertical deflection of the electron as it just exits the plates, in millimetre, to three decimal places.
✓ Verified answer: 0.44checked by our engine — not a guess
Step-by-step solution
Field between plates E = V/d = 50/0.04 = 1250 V/m.
Acceleration a = eE/m = (1.6e-19)(1250)/(9.1e-31) = 2.198e14 m/s^2.
Time in field t = L/v = 0.04/2e7 = 2e-9 s.
Vertical deflection y = 0.5 a t^2 = 0.5(2.198e14)(2e-9)^2 = 0.5(2.198e14)(4e-18) = 4.396e-4 m = 0.440 mm (well within the 20 mm half-gap, so the electron exits).
Final answer0.44
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