Electrostatics 2014 Level 1: Basic Charges The universe is made up of basic particles that combine and seperate to form all matter. These basic particles (as you learned in chemistry) consist of protons, electrons and neutrons. Electrons are small masses with a negative charge. Protons have a positive charge and a comparatively larger mass. Neutrons have the same mass as protons, but no charge. For the sake of this course, we will largely be dealing with protons and electrons. Neutrons are rarely mentioned. Charge on the Particles We measure charge in Coulombs (C). The smallest charge in the universe (that we will deal with in this class) is 1.6 10 19 C. We call this the elementary charge, because the rest of the universe is built upon positive and negative multiples of this charge. The negative elementary charge is the electron, which a charge of 1.6 10 19 C. The positive elementary charge is the proton with a charge of +1.6 10 19 C. We symbolize an elementary charge with a lower case e. When we talk about charge, an electron, therefore, is e and a proton is +e. Most of the time, matter does not have any charge. This is because the protons and electrons perfectly cancel out. In some situations, however, an atom might gain or lose electrons. If an object lost some electrons, it has more protons than electrons, and therefore has a positive charge. If an electron has gained electrons, it has an overall negative charge. Notice we never discuss gaining or losing protons. Key Idea Objects only charge through the movement of electrons, not the movement of protons. A typical atom has the same number of protons and electrons, so it is effectively neutral. Sometimes an atom will have an unbalanced charge, however, because it lost or gained an electron in a chemical process. This is called ionization. An ion is just a term for any atom that has a charge- this could mean it has a slightly positive charge or a slightly negative charge. The most important thing you need to remember throughout this entire section is the Law of Conservation of Charge, which states charges cannot be created or destroyed. They can be exchanged, passed around, added and subtracted to objects, but overall, you can t destroy charge any more than you can destroy matter.
Practice Problem: Finding the Number of Charges Some materials, called conductors, allow charges to move around rather freely. Insulators are the opposite. If you stick a bunch of electrons on an insulator, it will keep them pretty much where you left them. Think of insulators as prisons, where you lock the charge in a particular cell. Think of conductors as pools of water, where the particles can swim away from each other (or toward each other) like fish. Opposite charges are attracted to one another. This means protons and electrons are drawn together. Similar charges are repelled by one another. Electrons will always try to move away from each other when given a chance, and the same thing happens with protons.
If you put a bunch of protons on a conducting sphere. In a fraction of a second they will move like this: Inside a Conductor Because the charges what to get as far away from each other as possible, they will always spread out along the outside of a conductor. This means that you will never have a charge inside on a conductor. It you put one there, it would immediately transfer to the outside. Pop survival quiz- you are in the middle of an Illinois field (very very flat) when a terrible lightning storm blows up. Where is the safest place to take shelter- under a very tall tree, in a nearby, quickly flowing stream, or a nearby chicken coop made of chicken wire? Let s explore what the best answer would be. Because the charges what to get as far away from each other as possible, they will always spread out along the outside of a conductor. This means that you will never have a charge inside on a conductor. It you put one there, it would immediately transfer to the outside. Key Idea There is never a net electric charge inside a conductor.
A Faraday Cage is a fancy name for a conductor that is hollow inside. If you place an object inside, it would essentially be the safe from any charge you would zap the outside with. The picture on the left is completely real. Many science museums have Faraday Cages like this one set up for shows. You should, of course, never ever try this on your own. A simple faraday cage can be created out of nearly any conductor. There is a growing market for fashionable Faraday Cages, as they will essentially make your phone unable to receive a signal. Supplemental: Fashionable Faraday Cages. Here is one example of people marketing this idea. http://www.technologyreview.com/view/421768/silence-smart-phones-atthanksgiving-dinner-with-a-foldable-faraday-cage/ Conduction There are a variety of ways to charge objects. The most common is conduction. Conduction (just like in thermodynamics) involves charging by touching. This is the type you loved as a kid, when you rubbed a balloon all over your head and pulled it away, watching your hair stick to the balloon. In this situation, you ripped electrons off your hair and transferred them to your balloon. Afterward, your (positively charged) hair was attracted to the (negatively charged) balloon. Induction Because particles in conductors move away from like charges (and move toward opposite charges) we can mess around with them a little. Imagine you have a metal sphere with positive and negative equally balanced on its surface. This sphere currently has a neutral charge (see the picture below on the left). Now, imagine that you brought a wand with a positive charge nearby (without touching it). What would happen? The protons can t move- they are stuck in place. But the electrons they are paired with can flow around in a conductor. If you bring a positively charged rod nearby, the electrons will be drawn to it. They will leave their protons and rush toward the wand.
This metal sphere now has one side positive and the other negative. The second you move the outside positive wand away, however, the positives and negatives would mix up again, and the sphere would go back to being neutral. This charging by separating charges (without touching) is called induction. What if we wanted that sphere to keep that charge? What if we wanted the object to permanently have more electrons than protons? To do that, we hook the sphere up to a ground. A ground is pretty much a wire that connects to the ground. The earth itself is a vast sea of positive and negative electrons. You can toss electrons into it, or draw electrons up out of it. When the wand is brought near, the electrons in the sphere rush toward the wand (like the previous scenario). Now, let s imagine we attach a ground to the sphere. Electrons can leave the earth and flow into the spherewhich they are drawn to do by the attraction of the positively charged wand. Once these electrons are up in the sphere, we disconnect the ground and move the wand away. The sphere has a (fairly) permanent negative charge. The same can be done to get the sphere to have a positive charge. In this case, we approach the sphere with a negative wand. The ground allows the electrons to run away from the negative charges on the wand (left). A quick note: object that have a positive charge on one end and a negative charge on the other (like the sphere when the wand was brought near) are polarized. Important: Before moving on to the video, make sure I have stopped by your table and shown you the electroscope.
Video Simulation: This video will help you visualize what is happening during a few complex electroscope demos. Make sure you watch it until you understand it. http://www.youtube.com/watch?v=-jsvzwc1doo Level 2: Coulomb s Law We ve talked about the fact that opposites attract and likes repel. In this section, we ll learn how to calculate how to calculate the strength of that attraction. What if, for example, we had two charges hanging out in space, a certain distance apart? How much attraction/repulsion would they feel? That s right, folks. We ve finally made it to an equation. Coulomb s Law F = kq 1q 2 r 2 q Charge, measured in Coulombs r Distance between the charges, measured in meters k Another sweet constant. This one is 9 x 10 9 N m 2 /C 2 Example Problem from The Physics Classroom Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them. Solution F elect = k Q 1 Q 2 / d 2 F elect = (9.0 x 10 9 N m 2 /C 2 ) (1.00 C) (1.00 C) / (1.00 m) 2 F elect = 9.0 x 10 9 N The equation above can only tell you the magnitude (the amount) of the force. It does not tell you the direction of the force (attraction or repulsion). When you calculate the force, you should always use the absolute value. You are going to need to keep track of whether it is repelling or attracting yourself using free body diagrams. Later on in this section, we will look at how to use trig and free body diagrams to keep track of more complex problems. For now, when you enter the charges into the equation, use their magnitudes (amounts, without the sign) and then ask yourself whether this would be a force of attraction or repulsion.
Example Problem Solution Superposition Of course, it couldn t be that easy. While you will sometimes encounter problems involving two objects attraction/repulsion from one another, you will much more often encounter problems like the one on the right. Forces (like the forces of electrostatic repulsion/attraction) are vectors, which means we need to take their direction into account when we are adding them together. Superposition is just a fancy way of saying adding vectors. Hold on to your hats, kids, because this section is going to take a little trig. Linear Superposition Before we dive into the trig, let s look at a problem where the particles are in a straight line. When you solve these, draw a free body diagram. Just a refresher, check out the free body diagrams below and make sure you are clear on where the net force came from. Now, try a problem involving Coulomb s Law. Remember to draw a free body diagram.
Example Problem Solution Supplemental: Watch Twu Solve Linear Superposition Problems This is not a required video, but if you are someone who likes to watch people solve problems, give this one a try. http://www.youtube.com/watch?v=bb4pdhuimzc Superposition in 2D Before we move on, make sure you find the net force in the situation below. That wasn t too bad, huh? Okay, now let s add in some trig. Remember to draw a free body diagram and break the vectors down into x and y components. If you have trouble remembering how to add vectors from last year, call me over and I can help you review. This is going to require a blast from the physics past and quite a bit of trig. Trig Review Looking for a quick trig refresher? Just want to take a break and watch a trig-based rap? Here you go. http://www.youtube.com/watch?v=t2upyylh4zo.
Review Problem DO NOT move on until you feel completely comfortable doing this. Remember that a net force includes a direction. a) Add the forces together and find the net horizontal force. b) Add the forces together and find the net vertical force. c) Find the net force including the direction. Solution Try this yourself before checking the solution below. First, break F 1 and F 3 down into their components (the parts of them that point in the x and y direction). I ve shown you how to do this with F 1 to help jog your memory F 1x = F 1 cos(55) F 1x = 7.3 cos(55) F 1x = 4.18 F 1y = 7.3 sin(55) = 5.98 When you ve done this for all the forces, add (and subtract) the forces to help you find the net force in the x and y directions. The work below shows this.
The forces in the x and y directions are therefore: Use Pythagorean to find the net force. You should get 11.3 N. But wait, there s more. You need to use trig to find the direction of the net force. Opposite over adjacent, son. If you did this right, you should get 22.7. Example Problem The distance between the 2nC and 3nC charge is 5 cm. Using the diagram above, find: a) The total horizontal forces acting on the 4nC charge. b) The total vertical forces acting on the 4 nc charge. c) Find the net force on the 4nC charge.
Solutions
Example Problem Princeton Review
Solution Brace yourself, it is about to get real. Don t look at the solution to this one until you have tried it on your own. from Princeton Review Solution
Level 3: Electric Field Strength Electric field strength is not a particularly difficult concept, but it is very abstract. I ve taught this for years and I ve only found one way that (sometimes) clicks with students. You will have to bear with me, because it is a little weird. Electric Field Strength gives us an indication of how attractive (or repulsive) a charge would be if another particle was placed nearby. It does not tell us about the force of attraction between two particles. It tells about one particle s ability to attract or repel at a particle position.
Here is the analogy I ve used in the past which has helped some people. Imagine you are standing a particular distance away from an attractive person. I ve put both genders here, so pick. Imagine someone you think is pretty attractive. You are standing a set distance from this attractive person. If you were both electrostatic particles, Coulomb s Law would tell us how attracted you are to each other. We could calculate the force pulling you two crazy kids together (or pushing you apart, depending on your charge). But what if we took you out of the picture entirely? This person is still attractive right? In this analogy, Electric Field Strength would let us calculate how attractive that person is in general (not just to you). Person is attractive in general, not just to you Electric field strength isn t about the relationship between two particles- it describes the attractive/repulsive ability of a single particle at a particular distance away from it. It s about how that particle influences the space around it. The Test Particle How do we calculate exactly how attractive/repulsive a particle is? Use the equation below. Electric Field Strength E Electric field strength, measured in N/C q charge of the particle k same constant as before r distance from the charge. E = kq r 2 Let s try a basic electric field strength problem, plug n chug Practice Problem What is the electric field strength 2 cm away from a 4 µc charge?
Answer 9 10 7 N/C. Don t forget to convert that 2cm into meters. What did we just calculate? We basically calculated the attractive/repulsive ability of the 4 µc charge 2 cm away. This tells us amount of force this object can exert per coulomb. That s what the answer 9 10 7 N/C means. If we put a 1 C charge at this spot (2 cm away), it would feel a repulsive force of 9 10 7 N. If we put a 2 C charge at this point, it would feel a repulsion of 18 10 7 N. If we put a 3 C charge at this spot, it would feel a repulsion of 27 10 7 N. In other words, the electric field strength gave us an indication of exactly how attractive/repulsive that 4 µc charge would be 2 cm away. What if we put a charge of 6 µc at a position of 2 cm away from the 4 µc charge? Is there a way we could use the electric field strength to calculate the force of repulsion between the two particles? Sure! Here it is: F = Eq E Electric Field Strength of a particle at a particular position q charge of a different particle F Force of attraction/repulsion between the particles Example Problem A +10µ C charge is placed in an electric field with a strength of 20, 000 N/C at the location of the charge. When released, how much electric force will act on the charge? Solution Once you know the electric field strength at a particular position, it is very easy to calculate the force that would act on particles that are put at that spot. Adding Electric Fields Electric fields can be added much the same way that electric force can be added. Both are vectors- which means you need to take their direction into account when you are adding them. The problem below demonstrates how this works. from Holt Physics Example Problem
Solution
Summary of What We ve Learned So Far Calculates a relationship between two charges F = kqq r 2 To convert E = F q Describes something about one charge E = kq r 2 Level 4: Visualizing Electric Fields Electric field strength is a vector, which means you need to take its direction into account (just like with forces). When we try visualize electrostatic forces, we often create free body diagrams. When we want to visualize electric field strength, we draw electric field lines. They look like this:
In this section, we are going to learn how to create and interpret electric field line diagrams. This might seem complicated, but it actually isn t. The Test Charge Let s image we have some large, random charge floating around in space. We want to figure to visualize what the electric field strength would be around the charge. How could we do this out? In physics, we get an idea of the electric field around it by seeing what happens to a test charge. A test charge is just a tiny hypothetical charge we will move around nearby to see how it would respond. The test charge itself won t actually be in the problem- it is just a tool we use to check for the electric field strength. Think of it as your electric field meter man, walking around the charge in question, testing out the electric field strength at various positions. A test charge is, by definition: Incredibly small and massless, so it won t influence the problem. Always positive. This is just a convention all physicists agreed to long ago, like deciding down was negative and up is positive. As you move the test charge around, ask yourself two questions: Which way is the electric field pushing the test charge? How hard is it pushing it (really hard, sorta hard, not that hard )? Electric field diagrams are qualitative (at least at this level) which means we don t care about numbers. We care about the general shape. Let s do this one together. On the picture below, draw an arrow showing the direction the electric field would push this charge. Use an arrow to show how strong the test charge would be.
If you did that right, it should look this this: Now, repeat that process for all the positions I have marked below. Remember, longer arrows mean greater electric field strength. Check with your group members to make sure they have something similar to you. You can see there is a general shape to the electric field above. The charge creates an electric force that pushes the test charge (which is positive) away. On the right, I show how we would draw the official electric field for this charge. Use this same logic to create the electric field diagram for a negative charge. Try to draw that below:
If you did it correctly, it would look like this: Now, all electric field lines are drawn as though they are attracting or repelling a positive test charge. What would happen if you were to put an electron in the electric field to the left? What would it do? What if you put an electron in the electric field to the left- what happens? Key Idea: Positive charges move in the direction of the field lines. Negative charges move against the field lines. As much as I m sure you d like to sit around drawing field lines for individual particles, I m sure you know what is coming. field lines for multiple particles. Before you move to the next page, try to draw the electric fields for the situations below. Imagine, again, what happens to test charges in order to figure this out.
If you did these correctly, they look this this: Interpreting Electric Field Lines In order to interpret electric field lines, it s important to know a few things about them. You may have already noticed some of these key features already. You will never have to memorize the list below, but taking time to learn them will make your life a lot easier (a lot like memorizing thermo processes made them a lot easier). Here are some basic rules for drawing/interpreting electric field lines: 1. Electric field lines do not cross. 2. Electric field lines come out of positive charges and go into negatives (think about the test charge). 3. The denser the lines, the greater the electric field strength. from Princeton Review