Given the electric field and time... what is the speed of the electron?

Question

An electron is accelerated by a constant electric field of 300N/C. Use the equations with constant acceleration to find the electron's speed after 1.00x10^-8s, assuming it starts from rest.

Answer 1

The electric field will cause the electron to accelerate due to the force acting on the electron.
The force caused by the electric field is,
F = q * E,
Where q is the charge on the electron (1.602 E-19 C) and E is the electric field.

From Newton’s second law,
Force = mass * acceleration
Where the force we are concerned with is the electric field’s force and the mass is the mass of the electron (9.11 E-31 kg).

A object experiencing a constant force (as is this case, assuming a uniform electric field) will accelerate at a constant rate (assuming v << c).
The change in velocity as a function of time of an object constant accelerating is,
(delta v) = a * t
Where a is the acceleration and t is the time the object has been accelerating.

Since the electron started from rest, its change in velocity will be equation to its instantaneous velocity at any point in time.

Putting all of these equations together, we can find the velocity of the electron as a function of time and of several known constants.

V = q * E * t / m
The velocity of the electron at time, t, equals the product of the charge on the electron multiplied by the electric field, divided by the mass of the electron.

At time = 1 E-8 seconds,
V = (1.602 E-19 C) * (300 N/C) * (1 E-8 s) / (9.11 E-31 kg)
V = 527552 m/s

So the electron is traveling at about 5 E5 m/s after 10 nanoseconds.

Answer 2

anticipate that the accurate and bottom of this article field are both plates and also you hearth the electron into the demonstrate screen contained in the middle : if the plate is l metres deep (into the demonstrate screen) then this is going to take l microseconds to bypass via and through this time that is seeing an acceleration from bottom to accurate of the demonstrate screen, in case you overlook about relativistic consequences ( which see the element lose slightly power via acceleration) then you definately can merely use distance moved = a*l*l/2 the position the acceleration is the electric powered field power divided via the mass of the electron. 1e6 m/s is merely about a million/three hundred the speed of sunshine so that you may want to be ok ignoring relativity. best of success edit: forgot about the proton! that is a lot extra large so gained't see a similar acceleration although this is shifting on a similar velocity so is being sped up (downwards this time) for a similar era of time