Published on January 9, 2008
Physics 121: Electricity & Magnetism – Lecture 2Electric Charge: Physics 121: Electricity & Magnetism – Lecture 2 Electric Charge Dale E. Gary Wenda Cao NJIT Physics Department Electricity in Nature: Electricity in Nature Most dramatic natural electrical phenomenon is lightning. Static electricity (balloons, comb & paper, shock from a door knob) Uses—photocopying, ink-jet printing Static Charge: Static Charge 1. How can I demonstrate static charge using an inflated balloon? Pop it. The sound it makes is due to static charge. Rub it on cloth, rug, or hair, then it will stick to a wall. Rub it on a metal surface, then use it to pick up bits of paper. Drop it and time its fall. If it falls slower than a rock, it is affected by static charge. Let the air out slowly. It will be larger than its original size due to static charge. Demonstrations of Electrostatics: Demonstrations of Electrostatics Balloon Glass rod/silk Plastic rod/fur Electroscope Van de Graaf Generator Glass Rod/Plastic Rod: Glass Rod/Plastic Rod A glass rod rubbed with silk gets a positive charge. A plastic rod rubbed with fur gets a negative charge. Suspend a charged glass rod from a thread, and another charged glass rod repels it. A charged plastic rod, however, attracts it. This mysterious force is called the electric force. Many similar experiments of all kinds led Benjamin Franklin (around 1750) to the conclusion that there are two types of charge, which he called positive and negative. He also discovered that charge was not created by rubbing, but rather the charge is transferred from the rubbing material to the rubbed object, or vice versa. Forces Between Charges: Forces Between Charges We observe that Like charges repel each other Opposite charges attract each other Electroscope: Electroscope This is a device that can visually show whether it is charged with static electricity. Here is an example charged positive. Notice that the charges collect near the ends, and since like charges repel, they exert a force sideways. You can make the deflection arm move by adding either positive or negative charge. BUT, we seem to be able to make it move without touching it. What is happening? - - - - - - Electrostatic Induction The Atom: The Atom We now know that all atoms are made of positive charges in the nucleus, surrounded by a cloud of tiny electrons. Proton charge +e, electron charge -e where e = 1.60210-19 C The Atom: The Atom We now know that all atoms are made of positive charges in the nucleus, surrounded by a cloud of tiny electrons. Proton Electron Proton charge +e, electron charge -e where e = 1.60210-19 C Atoms are normally neutral, meaning that they have exactly the same number of protons as they do electrons. The charges balance, and the atom has no net charge. 2. Which type of charge is easiest to remove from an atom? Proton Electron The Atom: The Atom Proton charge +e, electron charge -e where e = 1.60210-19 C 3. If we remove an electron, what is the net charge on the atom? Positive Negative In fact, protons are VASTLY more difficult to remove, and for all practical purposes it NEVER happens except in radioactive materials. In this course, we will ignore this case. Only electrons can be removed. If we cannot remove a proton, how do we ever make something charged negatively? By adding an “extra” electron. Glass Rod/Plastic Rod Again: Glass Rod/Plastic Rod Again We can now interpret what is happening with the glass/plastic rod experiments. Glass happens to lose electrons easily, and silk grabs them away from the glass atoms, so after rubbing the glass becomes positively charged and the silk becomes negatively charged. Plastic has the opposite tendency. It easily grabs electrons from the fur, so that it becomes positively charged while the fur becomes negatively charged. The ability to gain or lose electrons through rubbing is called Triboelectricity. Tribo means rubbing Triboelectric Series: Triboelectric Series asbestos rabbit fur glass hair nylon wool silk paper cotton hard rubber synthetic rubber polyester styrofoam orlon saran polyurethane polyethylene polypropylene polyvinyl chloride (PVC pipe) teflon silicone rubber Most Positive (items on this end lose electrons) Most Negative (items on this end steal electrons) Insulators and Conductors: Conductor Insulators and Conductors Both insulators and conductors can be charged. The difference is that On an insulator charges are not able to move from place to place. If you charge an insulator, you are typically depositing (or removing) charges only from the surface, and they will stay where you put them. On a conductor, charges can freely move. If you try to place charge on a conductor, it will quickly spread over the entire conductor. Insulator Insulators and Conductors: Insulators and Conductors 4. Which of the following is a good conductor of electricity? A plastic rod. A glass rod. A rock. A wooden stick. A metal rod. Metals and Conduction: Metals and Conduction Notice that metals are not only good electrical conductors, but they are also good heat conductors, tend to be shiny (if polished), and are maleable (can be bent or shaped). These are all properties that come from the ability of electrons to move easily. Path of electron in a metal This iron atom (26 protons, 26 electrons) has two electrons in its outer shell, which can move from one iron atom to the next in a metal. Van de Graaf Generator: Van de Graaf Generator Rubber band steals electrons from glass Glass becomes positively charged Rubber band carries electrons downward Positively charged glass continues to rotate Wire “brush” steals electrons from rubber band Positively charged glass steals electrons from upper brush Sphere (or soda can) becomes positively charged—to 20,000 volts! Electric Force and Coulomb’s Law: Electric Force and Coulomb’s Law We can measure the force of attraction or repulsion between charges, call them q1 and q2 (we will use the symbol q or Q for charge). When we do that, we find that the force is proportional to the each of the charges, is inversely proportional to the distance between them, and is directed along the line between them (along r). In symbols, the magnitude of the force is where k is some constant of proportionality. This force law was first studied by Coulomb in 1785, and is called Coulomb’s Law. The constant k = 8.98755109 N m2/C2 is the Coulomb constant. r q1 q2 q1 q2 Electric Force and Coulomb’s Law: Electric Force and Coulomb’s Law Although we can write down a vector form for the force, it is easier to simply use the equation for the magnitude, and just use the “like charges repel, opposites attract” rule to figure out the direction of the force. Note that the form for Coulomb’s Law is exactly the same as for gravitational force between two masses Note also that the mass is an intrinsic property of matter. Likewise, charge is also an intrinsic property. We only know it exists, and can learn its properties, because of the force it exerts. Because it makes other equations easier to write, Coulomb’s constant is actually written where e0 = 8.8510-12 C2/N-m2 is called the permittivity constant. Note BIG difference, There is only one “sign” of mass, only attraction. Spherical Conductors: Spherical Conductors Because it is conducting, charge on a metal sphere will go everywhere over the surface. You can easily see why, because each of the charges pushes on the others so that they all move apart as far as they can go. Because of the symmetry of the situation, they spread themselves out uniformly. There is a theorem that applies to this case, called the shell theorem, that states that the sphere will act as if all of the charge were concentrated at the center. These two situations are the same Note, forces are equal and opposite Insulators and Conductors: Insulators and Conductors 5. Two small spheres are charged with equal and opposite charges, and are placed 30 cm apart. Then the charge on sphere 1 is doubled. Which diagram could be considered to show the correct forces? -q A. B. C. D. E. 2q Case of Multiple Charges: Case of Multiple Charges You can determine the force on a particular charge by adding up all of the forces from each charge. Forces on one charge due to a number of other charges Charges in a Line: Charges in a Line 6. Where do I have to place the + charge in order for the force to balance, in the figure at right? Cannot tell, because + charge value is not given. Exactly in the middle between the two negative charges. On the line between the two negative charges, but closer to the -2q charge. On the line between the two negative charges, but closer to the -q charge. There is no location that will give force balance. Let’s Calculate the Exact Location: Let’s Calculate the Exact Location Force is attractive toward both negative charges, hence could balance. Need a coordinate system, so choose total distance as L, and position of + charge from -q charge as x. Force is sum of the two force vectors, and has to be zero, so A lot of things cancel, including Q, so our answer does not depend on knowing the + charge value. We end up with Solving for x, , so slightly less than half-way between. x L Summary: Summary Charge is an intrinsic property of matter. Charge comes in two opposite senses, positive and negative. Mobil charges we will usually deal with are electrons, which can be removed from an atom to make positive charge, or added to an atom to make negative charge. A positively charged atom or molecule can also be mobil. There is a smallest unit of charge, e, which is e = 1.60210-19 C. Charge can only come in units of e, so charge is quantized. The unit of charge is the Coulomb. Charge is conserved. Charge can be destroyed only in pairs (+e and –e can annihilate each other). Otherwise, it can only be moved from place to place. Like charges repel, opposite charges attract. The electric force is give by Coulomb’s Law: Materials can be either conductors or insulators. Conductors and insulators can both be charged by adding charge, but charge can also be induced. Spherical conductors act as if all of the charge on their surface were concentrated at their centers.