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Transcript

Physics 102 Spring 2008 Lecture Notes: Giancioli, Chapter 16 16-1 Electric Charge and its Conservation There are two types of electric charge: positive and negative Like charges (objects with an extra amount of the same type of charge) repel, or push away from each other Unlike charges (objects with an extra amount of opposite types of charge) attract, or pull toward each other Electric charge is conserved, no charge can be created or destroyed in any process. Even though we say an certain amount of negative charge will “cancel out” an equal amount of positive charge, all of the charges still exist. The overall sum of the charges will be neutral. 16-2 Electric Charge in the Atom In an atom, positive charge is carried by particles called protons that are located in the nucleus. Electrons carry negative charge and zip around the nucleus, occupying a region of space called an orbital. The charge on a proton is exactly equal to the charge on an electron, but opposite in sign. Neutral atoms or molecules, therefore, have an equal number of electrons and protons. Polar objects have an uneven distribution of electric charge, even though they are neutral overall. Water molecules are polar. They attract the extra electrons on negatively charged objects, and drop these electrons off easily on positively charged objects. Water in the air, therefore, tends to neutralize charged objects by redistributing the charge. 16-3 Insulators and Conductors Conductors- materials in which electrons can move freely, allowing charge to distribute itself evenly throughout the material. Insulators- materials in which electrons can not move freely. Conductors Insulators 16-4 Induced Charge, Charging by Conduction and Induction A charged object can polarize a neutral object, so that charge is unevenly distributed in the object. In an insulator, the polarization is local to each atom or molecule. In a conductor, where charges can move, opposite ends of the object will have opposite charge. 16-5 Coulomb’s Law The force between two charged objects always points along the line joining the two objects. If the objects have the same sign charge, the force on the first points away from the second, and vice versa. If the objects have the opposite sign charge, the force on the first points toward the second, and vice versa. The magnitude of this force is equal to the following: If we plug in a positive number Q for positive charges, and a negative number Q for negative charges, the force will come out to be repulsive between the charges when it is a positive number, and attractive when it is a negative number. Superposition: the principle of superposition states that we can find the total, or net effect of some phenomenon by adding up individual effects. For the electric force between charged objects, this means that the net force on an object is just the sum of the forces due to each charged object in the vicinity. 16-6 Coulomb’s Law in 2-D Problems (using vectors) Using superposition, we can find the net force on a charged object due to other charged objects nearby. We do this by adding the force vectors between our original object and the other charged objects. Example 16-4 Find the total force on Q3 from Q1 and Q2. The three charges form a 60/90/30 triangle, with Q3 at the 60 degree corner, .60 m from Q1, Q1 at the 30 degree angle, .52 m from Q2, and Q2 at the 90 degree angle, .30 m from Q3. Q1 - +65 microC, Q2 = -86 microC, and Q3 = +50 microC. To solve this problem, first find the force from Q1 on Q3 and the force from Q2 on Q3. You can then break these vectors up into their components, and add them to find the net force. 16-7 The Electric Field Scientists created the idea of a field to explain forces between objects that don’t actually touch each other. We say an object creates a force field throughout the space around it, and this field then touches and exerts a force on objects nearby. We would like the electric field created by a charged object to only depend on the object itself. Then we can look at how this field will affect other charged objects. In general, this field will not be uniform throughout space, it will depend on how far away you are from the charged object. We define the electric field as the force a charged object would exert on another charged object at that point, divided by the charge of the second object: The vector we end up with, E, has a magnitude and direction that depend on our original charged object and how far away from it we are, but does not depend on the charge of the second object. We now have a way to calculate the force our first charged object will exert on any other object, and the direction of this force: We multiply the electric field vector due to the first object at the location of the second object by the charge of the second object.