An electron is projected with an initial speed 1.70×106 m/s into the uniform field between two parallel plates that are 1 cm apart. Assume that the field between the plates is uniform and directed vertically downward (positive to negative), and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.

If the electron just misses the upper plate as it emerges from the field, find the speed of the electron as it emerges from the field?

Question

An electron is projected with an initial speed 1.70×106 m/s into the uniform field between two parallel plates that are 1 cm apart. Assume that the field between the plates is uniform and directed vertically downward (positive to negative), and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.

If the electron just misses the upper plate as it emerges from the field, find the speed of the electron as it emerges from the field?

irishboy123 · Answer

the upwards force on the electron will be given by $$F = Eq_e - m_e g$$

this will be a constant force as the electric field will be constant inside the parallel plates, so  first, you can also say that $$F = m_e \ a$$ so that upward acceleration, a, is:$$a =\frac{Eq_e - m_e g}{m_e} = E\frac{q_e}{m_e} - g$$ 

you can also use the equations of motion, i suggest here $$v^2 = u^2 + 2ax$$
initial [ie vertical] velocity u = 0, x = 0.5cm, v is what we want, ie the vertical component of velocity, and we also have an expression for a; but note that you have not provided a field strength.

for this to be answerable, we need to know either the field strength, or indeed the length of the plates.  if we have plate length, the question becomes considerably simpler.