Your Conceptual Goals for this section: E Fields

Fields (electric or otherwise):

The question of what a field is and why we need these beasts is a actually quite rich. We will explore some of the philosophy behind this concept in class but if you would like some reading on the topic here are some suggestions.

stackexchange: This is a great discussion of physics as equivalent in some way to trying to understand the 'code' of the universe. Here is one of their threads addressing the concept of fields.

Here is a longer pdf document walking through the history of fields as an idea and the motivation. You will need to form your own understanding of what fields are and why they are valuable as a concept if not a reality.

Here's the thought exercise we will discuss. If the sun were to start moving in some new direction how long would it take for the earth of any of the outer planets to notice the change in the direction of gravity? What are the possible answers? How can you test these different answers? [results of tests will be shared in class]

Electric Field (E):

Regardless of the philosophic roots of the idea of fields we detect the presence of fields by measuring forces (or the behavior caused by forces) on known objects. For electric fields we must use a test object which feels an electrostatic force (Coulomb force). That suggests that the test object would be a charge brilliantly labeled as q_test. I often think of this as my test charge on a string that I keep in my pocket.

We define the E field to be the force per unit of charge (N/C) which can be written E = F/ q_test. You will note that the E field points the same direction as the force on a + charge. We can carry our little test charge all over the world and measure the field at every point in space.

On average there is an electric field near the surface of the earth that points downward and has a magnitude of around 150 N/C.

What is a comparable definition of the gravitational field (not force!)?

Once you know the E field then what?

Once you know the E field at a particular point then you can predict what the force (magnitude and direction) on any charge placed at that point. This charge I like to label as a field charge (q_field) inidcating that it is a charge which experiences the field rather than the q_test we used to empirically determine the field.

In this context F_qfield = E q_field which is the value of knowing the E field at that point.

This is very much like knowing that F_g = mg from PH211.

Imagine you have two charges at some distance from each other....

If we treat the +5 μC charge as the test charge can you figure out the E field at that point in space? Do so.....

What about the E field at the location of the -3 μC charge?

Now I replace the -3 μC charge with a +8 μC charge. What is the magnitude and direction of the force on it?

As you have no doubt noticed there is a pattern to this....

In this case they use q_o instead of q_field but the meaning is the same.

Field Representations:

I will no doubt link this math/physics simulation site maintained by Paul Falstad many times in other parts of this class. He really has done a huge service for the physics learning community. Thanks Paul!! He used to have a personal page but I'm not finding it at this time.

For this section of our course this 3D electrostatics simulation is a great starting point. Set the display to 'Field Vectors' and then explore the many different charge distributions that he has built. Think about the direction and intensity of the field at different points and explore what they look like when you slice them.

Here are some particular problems that we will help us with that exploration.

Single Charge (both + and -):

What do the fields look like around a single + or - charge? How are the vectors different if the charge has a greater or lesser magnitude?

Now lets consider how this might be represented abstractly with what are called electric field lines. This is a way of summarizing the collection of E field vectors.

Here is a different electric field simulator from that web page. Place a single + charge in the middle of the screen. Then stack a couple more on top of it. Does the simulation do the right thing? Compare with Falstad's simulation.

If you want to have a little fun with fields and charges here is a E field hockey game. Simple on first level but gets challenging quickly:)

Dipole Field:

A dipole is a common object to find in the natural world. In it's most basic form it looks like this

...where the charges are presumed to be of the same magnitude. Sketch a dipole and draw the axis of the dipole (the line that passes through both charges). Now sketch the perpendicular bisector of the dipole (perpendicular to the axis at a point half way between the charges). Pick a point along the perpendicular bisector but away from the axis. Sketch the contribution to the E field from each charge. What do you notice about the symmetry? Is this constant everywhere on the bisector? Consider points near either charge -- is the other charge an important contributor to the total E field near one of the charges? Why?

Now go explore the vector and field line representations of a dipole on the Falstad simulation. What does this look like from magnetism?

Two of the same charge:

Change the charges in the previous picture to be the same sign and repeat the process of exploring the total E field on the axis and on the bisector. What is your qualitative sense of the shape of the E field in this case?

Go explore and confirm on the Falstad simulation!

What you should be able to sketch:

As a competent geek/nerd/science person you should be able to sketch each of these four field configurations (in the field line representation) with confidence....+, -, dipole, two charges (same).

Multiple Charges:

Just like multiple forces in the previous section: Do a vector sketch, sketch the components, add the vectors. Done!

Integration:

Just like Coulomb Force problems in the previous section. Follow the integration frame and don't be thrown off by the fact that there is usually no charge where you are asked to find the field. Practice, practice, practice....