An electron (mass m = 9.11E-31 kg) is accelerated in the uniform field E (E = 1.31E+4 N/C) between two parallel charged plates. The separation of the plates is 1.08 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, as seen in the figure below.

(Figure is just an electron between ideal capacitor plates)

With what speed does it leave the hole?

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I understand that force = Electric field x charge of the particle
I assume that the charge is going to vary as the electron moves away from the negative and towards the positive plate, which tells me I should use calculus and solve it as an integral?

I do well in calculus but I don't understand how calc will help me solve for speed in this case.

My professor doesn't have office hours until long after the homework is due, and "doesn't use any form of electronic communication". (Yes. This issue will be brought up with his supervisor if it continues.) I appreciate any conceptual help you guys can offer.

 

Solved.

I mistakenly solved for accel and stopped. The correct answer is found by solving for accel (electric field x charge of electron) dividng by mass of the electron for acceleration, then using:

Vf^2=Vi^2+2aS Where S is change in position, Vf is velocity final, and Vi is velocity initial (0 in this case)

 

No calculus required because as the electron moves away from the negative plate it approaches the positive plate, the reduction in field from the negative is compensated by in the increase in field from the positive plate, thus creating a constant force.

 

You are mixing up several concepts here. The plates have established charges on them that aren't changing. The electron is never on either plate anyway.

How about considering it from an energy perspective.

What is the voltage difference V between the plates?

How much energy is imparted to a charge Q moving through a potential difference V?

What is the kinetic energy of an electron traveling at a speed S (assume non-relativistic).