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Transcript
Electric potential energy and electric potential . Today we wax mathematical for awhile, but stick with me, in the end we will have a few new powerful concepts and simple formulas to work with. Work and kinetic energy. Recall from mechanics the formula that we derived from the equations of motion for constant acceleration which arise from a constant force acting along (parallel to) the line of motion. We obtain the formula by solving for time in the second equation and substituting this value of time into the first equation to eliminate the time variable. Ever wonder where we get our definitions of work and kinetic energy? Multiply the formula by Recognize anything? The kinetic energy and the work terms! The formula is none other than the work-energy theorem in disguise. What if the force is not parallel to the displacement? Recall from mechanics the more general case of work done by a constant force acting through a displacement , with angle between the vectors Gravitational potential energy. For the gravitational acceleration field The work done by the gravitation field on a body of mass , acting through a displacement is Are you wondering why I use the subscript G (we did not use it in mechanics)? Because soon we will be using the subscript E for the electric force! Note that the change in elevation (height) is given by It does not matter what path the body takes, straight up or down, along an incline, or some curved path: all that matters is the change in elevation, which is the displacement parallel to the field, thus In mechanics, we noted something special about the gravitational field: it conserves energy. All of the energy “stored” in the field when you lift a book is recovered as energy of motion when the book falls. If the potential energy of a field is path independent, it is a conservative field. We defined the change in gravitational potential energy as the negative of the work done by the gravity field acting on a body of mass through a displacement Here, it is worthwhile to remember that , the change in elevation, can be positive or negative, corresponding to the body moving up or down. If we define a zero reference (we define the potential energy to be zero at a certain elevation) then we omit the symbol write and think of it as an “absolute” potential energy that everyone in the universes agrees on. There is no such thing as an absolute potential energy, there is only relative potential between two points, but that does not stop us from pretending we have an absolute! Here, “absolute” means simply that everyone “agrees” on a zero reference. Now let’s talk about the work done by a uniform the electric field and we define the change in electrical potential energy as the negative of the work done by the electric field on a body of charge We take things one step further and define “electric potential” and define a new unit You are all familiar with volts, as in “1.5V battery”. What does that mean? If a charge of moves from the top of the battery to the bottom (say along a wire), it experiences a change in potential and a change in potential energy of Supposed you attach the battery to parallel plates and let an electron “fall” upward through the potential difference. How fast will the electron be moving? Let If we discharge the 1.5V battery through a wire, does this mean the electrons end up moving this fast? No, because a wire is filled with atoms, it is an obstacle course; the electron bumps into atoms all along its way and loses energy, causing the atoms to vibrate more (heat up). By the time the electron reaches the bottom, its tongue is hanging out, it is tired and flops onto the ground motionless, having lost all of its energy to heat. What did we learn today? The electric potential , the potential field electric field and its relationship to the , for two cases: 1) a uniform electric field, and 2) the electric field of a point charge. We introduced two simple handy formulas If you are given the voltage (the potential) at points A and B, the potential difference can be used to find the change in potential energy experienced by a charge as it moves from A to B, which can be used in the work-energy theorem to analyze the motion of the charge. Finally, we discussed how the electric field is a conservative field, which means that energy is conserved by the field. As with the gravitational field, all of the energy “stored” in the field is given back, none is lost to friction (we neglect electromagnetic radiation produced by the relative acceleration of charged particles; some energy is carried away by radiation). Exam Friday, lookup your exam location on myWPI, it is based on your section number!