Find the vertical electric field between two horizontal plates

Question

An electron penetrates the region between two uniformly charged horizontal plates, but oppositely signed. Its initial speed, at half distance between the plates is 2×10 ^6 i m/s. The plates have a length of 4 cm and are 1.6 cm apart. In the whole region between the plates, the electric field ́ is uniform and perpendicular to the plates. (a) what is the maximum modulus that the vertical electric field can have so that the electron does not touch any plate?

The answer is 228 N/C but I'm not too sure how they got that?

Answer 1

Hi Alara E.,

I won't do the math, but essentially the electron is travelling horizontally, at constant velocity, and the electric field (supplied by the capacitor charge and reduced proportionally by the modulus) supplies a let's say downward force which causes a downward acceleration (gravity is negligible by comparison). That's just a parabolic path; you should assume that the inital condition is the vertex of the parabola. If the velocity were in any other direction the problem wouldn't make sense, would it, the electron would eventually be drawn to one of the plates.... think you can handle the math for acceleration, and the geometry of the resultant path, to "graze" the lower plate?

-- Cheers, --Mr. d.