Electric Fields

[Electric Fields]

Topic Elements

Measurements and Standards
1-D Motion
Vectors
2-D Motion
Forces & Newton's Laws of Motion
Work & Energy
Momentum (& Conservation)
Rotational Motion
Thermodynamics
Vibrations & Waves
Sound
Electric Force & Fields
Capacitance &
Direct Current Circuits
Magnetism
Reflection & Refraction

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Introduction

Electrostatics delves into a whole new world to explain to us the workings of electricity, current, fields, and particle physics. It is strongly tied to magnetism, which can be explained by attractive and repulsive forces.

Electrical Charges

Attractive and replusive? How would that make electricity? Lightning is a special situation in which...ahhh well, let's get into the basics before we discuss that.

History: the development of the concept "electron"

Every discussion has started with explaining or pointing out observations in static electricity

We learn:

that electric charge is causing static electricity
that there are two types of electric charge

+	positive charge [caused by protons]
	color convention: blue
-	negative charge [caused by electrons]
	color convention: red

that an object is neutral if the number of + and - charges present are equal
that by rubbing or other methods of contact will conduct electrons
that electrons are the only charged particles that are added or removed (protons remain in the object)
the terms: an object that has more electrons than protons is negatively charged and that an object that has more protons is positively charged
that the flow of electrons is what causes a current
that we denote charge by the symbol q or Q
[q] = 1 Coulomb = 1C

Behavior of Charged Objects/Particles

Basic rule of interaction between negative and positive charges: Opposites attract, like charges repel

Charge is spread out uniformly throughout the body of the object. The positive cancels out the negative. That constitutes a neutral body. However, when a charged object is brought near, you can expect the opposite charges to move toward each other.

When there is contact with a charged body, the electrons flow to the other.

And if you don't have the two objects or particles in physical contact, the charges just try to get close to each other as possible, thus creating poles. We call 'em dipoles because two charges separated into concentrated areas make two poles.

Well what suddenly sprung to mind? North pole vs. south pole of the earth maybe? Yeah well... don't jump there yet. You can think of charge dipoles like that but you can't use charged objects as a reason in explaining the earth's poles. They are manifestations of magnetic fields. But if you want to do that, hop on over to magnetism and read up, touch up, whatever.

In case I lost you with all this rambling, if you got the idea that moving electric charge (negative because electrons are the ones that move) is called a current (like a river current) then you're right on.

Conductors vs. Insulators

Electrons move through materials, creating a current. But when you think about it, how come you aren't zapped by everything you touch. (You could say duh, it's because it's not charged) If you touch a normal household wire (assuming it isn't shooting sparks =]) you don't get shocked.

Wire is metal that is usually wrapped around with plastic or some sort of insulator. There are terms: conductor and insulator, conduction and insulation.

Metal is a common conductor. The explanation digs back into chemistry, and if you want to think back that far (as you can tell, I haven't touched chemistry in a while...let's keep the hydrochloric acid in the bottle now...) Metals (most metals) have loosely bound electrons in their atoms. When electrons enter the metal, other electrons are displaced and flow out of the metal. Well, that's the basic way of looking at it...

Insulators are just the opposite, they inhibit the flow of current and are often used as a shield (in wiring). Charge isn't blocked, as it may be implied by this term but once the charge tries to go through the insulator it stops there and there is little flow. (Thats why you still get static electricity from those annoying plastic things. Does anyone know what I'm talking about?)

Coulomb's Law

Ok, lets get back to the nitty-gritty. So we know about the positive and negative charges. We also know that they attract and repel. That if you didn't notice (*nudge, nudge*) was reminiscent of forces and...yeah, gravitational fields! =)

Think back...to Newton...

His inverse square law of universal gravitation.

F =	Gm¹m²
	d²

Similarly there is the attraction between charges. The difference between gravitational and electrical forces is that electrical forces can be either attractive or repulsive whereas gravitational forces will always be pulling.

But Charles Coulomb is given credit for establishing the fundamental law of interaction (forces) between two stationary charges. He established that:

there is an inverse proportion to the square of the distance between the two charges
there is a direct proportionality to the product of the magnitudes of the charges
opposite charges attract, like charges repel

What would all this mean?

F = k	\|q₁\|\|q₂\|
	r²

where:

F is the magnitude of the force (remember force is a vector)
k is a constant (called Coulomb's Constant) found to equal 9.0 x 10^-9 Nm²/C²
q (1 and 2) are the the charges of each particle
r is the distance between the two stationary charges

[aquapulse.gif] Coulomb vs Cavendish

Charge It!

Credit cards? No. I mean, I'm telling you that when a charged object comes in contact with a neutral object, there'll be a flow of charge. (But why would it if an object is happy and perfectly neutral?) When the two objects make contact, you can sorta think of it this way. The two are one big object whose charge distributes itself uniformly throughout the "combined body." Although I said this relationship exists for charged and neutral, it also applies for charged and charged. Sorta obvious but, if there are two neutral bodies, charge isn't going to do anything so nothing happens when you touch 'em together.

Principle of Superposition [Revisited]

Getting a case of deja vu yet? Hehe, it's all a part of the sciences. Isn't it just cool how things overlap? Err...well that's one thing; In the study of electromagnetism (electricity and magnetism...they're pretty intertwined), you learn that it's always one way or the other. You can't superimpose one charge over the other. As you've seen in graphs and such, attracted or repelled charges have a definite direction of travel. But can two like charges cross paths?

Hmmm...well how can we answer that yet? I haven't told you much about electric fields yet.

Electric Fields

Charged particles exude fields when stationary. Electric fields basically exist around charged particles. When in the presense of another charge, these fields show the behavior of the particles' interaction (in terms of forces).

We must bring up this rule once again:

Opposite charges attract; Like charges repel

We show fields in lines. This is an isolated charged particle. The lines have a direction of "flow" which depends on the type of charge.

The only difference here about the field lines of these isolated charged particles is that the positive charge has field lines pointing out whereas the negative charge has field lines pointing in.

When you introduce more particles the interactions are thus bent according to the rule stated above:

Opposites Attract

Field lines flow from positive to negative
Like Repel

Field lines bend away from each other

E = k	\|q\|
	r

Electric Charges in JAVA

Electric Field Equations

E =	\|F\|
	\|q\|

where q is the charge of the particle entering the field of the first particle.

In another form (by plugging in the equation for force)

E = k	\|Q\|
	r²

where Q is the charge of the first particle exerting the field.

Electrostatic Equilibrium

This topic is simply an application of some rules that best be understood and memorized. We refer to conductors. Their loosely bound electrons move around the metal but if there is no net flow/motion of electrons in the conductor, several rules describe the situation.

there is 0 electric field inside the conductor
any surplus charge (i.e. not neutral) would reside on the surface of the conductor
the electric field outside a charged conductor is perpendicular to the surface
charge tends to accumulate at sharp points if the conductor has an irregular shape

What happens if you have a hollow conductor shaped like a sphere with an opening on top and drop a charged object inside? (This is similar to Michael Faraday's ice-pail experiment)

Using an electrometer to measure charge on the surface of the hollow conductor, Faraday was able to show that the surplus charge on a conductor resides on the surface.