Question

A beam of electrons is shot from left to right (+x direction) at a speed of 3 x 10⁵ m/s through a pair of plates that are 3 cm apart and are uniformly charged. They produce a force of 4.8 x 10^–17 N upward on the electron (+y direction).   So that our results are unambiguous, vectors pointing from left to right will be called +x, and from bottom to top (along the surface of the paper) will be +y.   Vectors pointing directly out of the paper will be called +z.
    (A) How large is the electric field experienced by the electron?
    (B) How large is the potential difference between the plates?
    (C) What way does the electric field point?
    (D) If the force were produced by electrons sitting on the bottom plate alone, and the beam is 1.5 cm away from the plate, how many electrons would be required?

Answer 1

Data Given

Speed of electron v= 3 X 10⁵ m/s, Force on Electron F = 4.8 X 10^-17 N

Part A) We know that force experienced by a charged particle in uniform electric field

Part B) Potential difference between the plates, given that d = 3 cm

Part C) Direction of electric field

As the force experienced by the electon is in +Y direction i.e Positive plate is the upper one. So direction of electric field is in -Y direction i.e Downwards.

Part D) Using Coulomb's law

where q = ne and e is charge on electron and n is no of electrons