Motion of Charged Particles in Uniform Electric Fields

Motion of Charged Particles in Uniform vs Non-Uniform Electric Fields

This formula is obtained from reversing the formula for electric field strength, E, which is electrostatic force divided by charge.
This is also the formula that was equated to the acceleration due to gravity in Millikan's oil drop experiment!

In a non-uniform electric field, a charged particle's acceleration is not constant.
This is because the electric field strength is constantly changing with it's separation from the source of the field.
However, in a uniform electric field, the electric field strength is uniform, meaning it is the same throughout the field.
This means that the acceleration of a charged particle in a uniform electric field is constant.

"Stationary" mobile charges will accelerate along a field line in a uniform electric field.
This means they will move towards either plate.

Because acceleration is constant, SUVAT equations can be used to determine how the charge moves.

We've discussed how acceleration is constant towards either plate depending on the field.
This is similar to the gravitational acceleration of free fall, which is constant and causes objects to move towards the ground.
The motion of a charged particle in a uniform field should be similar to that of projectile motion!
The speed of the particle can be separated from the perpendicular acceleration due to the field.

As a particle moves through a uniform field, it will deflect towards either plate.
The amount of deflection depends on the mass, charge and speed of the particles.
Particles of greater mass will need more force to be moved.
Particles of greater charge will be more susceptible to movement as they experience greater electrostatic force.
Particles of greater speed will spend less time in the field, and thus be under the effect of the field for a smaller duration.

Keep in mind that an uncharged particle such as a neutron experiences no force in an electric field and will therefore travel straight through the plates undeflected.

Experiments with charged particles will involve a large numbers of particles moving together with the same velocity as a particle beam.

In the above particle emitter, electrons are shot out of an electron gun to create an electron beam.
If a potential difference is connected across the X plates, then the particle is deflected either to the right or to the left.
If a potential difference is connected across the Y plates, the beam is deflected up or down.

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