Course:SCIE001/Physics/Reading Guides/Chapter 27

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27.1 Electric Field Models

This chapter mainly talks about how we draw electric field. In the top half of the page 819, it notes some of the useful field models and briefly notes how “useful” these models can be. For example, models with “infinite” length can actually be useful in some circumstances.

Limiting Cases and Typical Field Strengths

This part tells us how to do draw the field strength if there is more than one sources of electric field. This part is mainly the vector summation. http://www.phys.hawaii.edu/~teb/java/ntnujava/vector/vector.html It’s a cool program describing the vector summation.

27.2 The Electric Field of Multiple Point Charges

27.2 talks about how to “mathematically” calculate the electric field with multiple charged sources.

The Electric Field of a Dipole

This section defines a dipole to be the electric field that two equal but opposite charges separated by a small distance, slightly different from the “high school Chemistry” dipole (the definition is still the same for the rigorous Chemistry according to Chris). They are just composed of “two” objects. There are two interesting properties in this situation. As shown in figure 27.7, the electric fields for the points that are located on either the same axis or a perpendicular plane are parallel to the dipole between two point charges. The equation 27.11 and 27.12 shows how to calculate such electric fields.

Picturing the Electric Field

Nothing special. It’s just the time to “Draw” the electric field using everything we’ve learned so far =)

27.3 The Electric Field of a Continuous Charge Distribution

It’s sometimes hard to describe a charge of an object by giving the actual charge of an object. For example, suppose there is an infinitely long rod with an infinite number of charges. That wouldn’t help. So we describe it by the density of those charges, such as linear charge density, and the surface charge density, in the assumption that the object are uniformly charged.

A Problem-Solving Strategy

Read the pink box. It helps =)

An Infinite Line of Charge

One important concept to note: the electric field decreases by the factor of 1/r for the electric rod, not 1/(r^2).

27.4 The Electric Fields of Rings, Disks, Planes, and Spheres

My first reaction after reading the title: OMG D=. In the end, not so bad. Note that “r” is used to indicate the “radius,” so the distancey is now described by “z”, which came from the “z-axis.”

A Disk of Charge

Through some expressions and integrals, we get the equation (27.22), which is as same as the equation (27.23). This is further simplied to the “approximation” (27.25). And now we see why we were keep using [epsilon-naught] form instead of the [coulomb’s constant] form. The “pi” cancels out, and it makes much cleaner to use [epsilon-naught] than the [coulomb’s constant].

A Plane of Charge

The equation (27.27) is the result as R->infinity.

A Sphere of Charge

Equation (27.28) shows that the charged sphere behaves exactly same as the point charge with the same centre.

27.5 The Parallel-Plate Capacitor

Well, we know that the charge made by plane is described by the equation (27.27), and we have two of them. That gives us (27.29), the electric charge between two parallel plates. Read the fringe field.

Uniform Electric Fields

One prime example of uniform electric fields is the electric field made by the ideal parallel-plate capacitors. I cannot think any other way. Inputs?

27.6 Motion of a Charged Particle in an Electric Field

Goodies. There is an electric field, and a charged particle. How does this particle move? That’s all about this subchapter.

Motion in a Nonuniform Field

So the textbook says that there are very complicated cases in a nonuniform field. But they only give us how to work out one of the easiest non-uniform field cases, a circular motion between two charged objects. Look at figure 27.27.

27.7 Motion of a Dipole in an Electric Field

Dipole in a Uniform Field

According to 27.33, there is no net force for the dipole in a uniform electric field. However, there is a torque. This causes all the dipoles to “align” with the external electric field. And hey, you know what? It’s a magnet! And what happens is that these aligned dipoles still create the electric field even after the external electric field is removed, and self-orient themselves into a magnet. These are called permanent dipoles.

Dipole in a Nonuniform Field

Again, a nonuniform field can be complicated. But they only talk about a dipole and point charge. Jumping straight into conclusion, they get drawn. Why? It can be worked out as a common sense, or you can read the section. It’s an interesting reading =)