Question

An electron is moving in the +x-direction with a speed of 5.0x10^6 m/s. There is an electric field of 3.0kV/m in the +x-direction. What will be the electron's speed after it has moved 1.00cm?

Answer 1

To determine the final speed of the electron after moving 1.00cm, we first need to calculate the acceleration of the electron due to the electric field:

Given:
Initial speed, u = 5.0x10^6 m/s
Electric field, E = 3.0kV/m = 3.0 x 10^3 V/m
Distance moved, s = 1.00 cm = 1.00 x 10^-2 m

The force experienced by the electron due to the electric field is given by:
F = qE
where q is the charge of the electron, and E is the electric field strength.

The acceleration of the electron can be calculated by:
a = F/m
where m is the mass of the electron.

The work done by the electric field on the electron is given by:
W = F * s

The work done on the electron is equal to the change in its kinetic energy, which can be calculated using:
ΔK.E. = 0.5 * m * (v^2 - u^2)
(where v is the final velocity we are trying to find)

Equating the work done by the electric field to the change in kinetic energy:
F * s = 0.5 * m * (v^2 - u^2)

Solving these equations simultaneously will help us determine the final velocity of the electron.