An electron enters the gap between the plates of a capacitor at the center of the gap traveling parallel to theplates at 2.0 x 106m/s parallel to the plates. If the gap has a width of 1.0 cm and the surface charge densityof the upper and lower plates are±1.0 x 10-6C/m2, respectively. How far will the electron travel beforehitting a plate? (Assume that the electric field is uniform inside the capacitor and zero outside.)

Question

Physics

Emanuel Sutton

24 June, 00:14

An electron enters the gap between the plates of a capacitor at the center of the gap traveling parallel to theplates at 2.0 x 106m/s parallel to the plates. If the gap has a width of 1.0 cm and the surface charge densityof the upper and lower plates are±1.0 x 10-6C/m2, respectively. How far will the electron travel beforehitting a plate? (Assume that the electric field is uniform inside the capacitor and zero outside.)

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Ashley Combs · Answer 1

How far will the electron travel beforehitting a plate is 248.125mm

Explanation:

Applying Gauss' law:

Electric Field E = Charge density/epsilon nought

Where charge density=1.0 x 10^-6C/m2 & epsilon nought = 8.85 * 10^-12

Therefore E = 1.0 x 10^-6/8.85 * 10^-12

E = 1.13*10^5N/C

Force on electron F=qE

Where q=charge of electron=1.6*10^-19C

Therefore F=1.6*10^-19*1.13*10^5

F=1.808*10^-14N

Acceleration on electron a = Force/Mass

Where Mass of electron = 9.10938356 * 10^-31

Therefore a = 1.808*10^-14 / 9.11 * 10-31

a = 1.985*10^16m/s^2

Time spent between plate = Distance/Speed

From the question: Distance=1cm=0.01m and speed = 2*10^6m/s^2

Therefore Time = 0.01/2*10^6

Time = 5*10^-9s

How far the electron would travel S = ut + at^2/2 where u=0

S = 1.985*10^16 * (5*10^-9) ^2/2

S=24.8125*10^-2m

S=248.125mm