Deflection Of Electrons In Electric And Magnetic Field

Question 1

What happens when an electrom just enters the path between the two electric plates?

Answer 1

The Electric field intensity acts downward on the electron as it passed through the plates; there is no horizontal force, hence acceleration for the horizontal component is 0.

Question 2

Describe mathematically the vertical displacement experienced by the electron as it just enters the plates.

Answer 2

F = ma = qE (force acting on electron is same as the electric force F = qE)

==> a = qE/m (m is mass of electron, q is charge)

from equation of motion:

y = v°t + ½at² ( initial velocity v° is zero, substitute the value for a)

y = ½(qE/m)t²

Question 3

Describe mathematically the horizontal displacement experienced by the electron as it just enters the plates.

Answer 3

Because there is no horizontal force, acceleration = 0

x = v°t + ½at² (V°x is initial velocity)

x = V°t

==> t = x/v°

Question 4

After deriving the expression for x-displacement, what is the new formula for y-displacement of an electron as it just enters the charged plates?

Answer 4

y = ½(qE/m) × (x/v°)²