Evans SPH 4U1

Unit 6: Electricity

Note 7: Motion of Charged Particles in Electric Fields

Reference: Chapter 7.6

In Non Uniform Fields:

So far we’ve looked at the electric charges, forces and fields produced by charged particles.  Now we will look at their motion.

·         A charge q1 experiences a Coulomb force

·         The charge will accelerate (Newton’s 2nd Law – when an external, unbalanced force acts on an object the object accelerates).

See if students can realize the problem of using this to analyze the charges motion. (i.e. as it moves r increases causing F to decrease)

·         Hence we use energy to analyze its motion rather than force and acceleration.

·         Consider q1 to initially be at rest. There will be electric potential energy between q1 and q2.  As the distance between q1 and q2 increase the electric potential energy decreases and q1 acquires kinetic energy.

At r the system has electric potential energy only since it is not moving yet..

In other words the charged particle moves in the electric field of q2 in such a way that the electric potential energy it loses is equal to the kinetic energy it gains.

Example: A charge, q1, of +1.0 x 10-9C with a mass of +1.0 x 10-6kg is at rest 10cm from a positive charge, q2, of +2.0 x 10-9C (assume they are in a vacuum).  What speed will the charge q1 have when it is 20 cm from the q2?

In Uniform Fields (ie. between parallel plates):

Motion of particles are even easier to analyze in uniform electric fields.

If the charged particle is moving in a uniform electric field which means acceleration is constant since the field is constant at any point between the parallel plates:

Between parallel plates whose plates are separated by d, the work done in moving a charge of q from one plate to the other is:

This amount of work is equal in magnitude to the change in electric potential energy and also the change in kinetic energy of the particle as it moves from one plate to the other.

Example: A capacitor is charged so that the potential difference between its two plates is 2000 volts. If an electron of mass 9.0 X 10-31 kg is released at the negative plate, with what speed does it hit the positive plate?

Note: The elemental charge of an electron is 1.6 X 10-19 C

Text: Page 368 #'s 1-5, Page 371 #'s 2,4,5