# energy - Physics 54 Electromagnetic Energy We all get...

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Physics 54 Electromagnetic Energy We all get heavier as we get older, because there's a lot more information in our heads. — Vlade Divac Overview We have previously discussed energy in the electrostatic feld, such as that in a capacitor. We Found that the energy can be thought oF as distributed in space, and we speak oF the energy in the E-feld, described by giving the energy per unit volume (energy density) at each point in space. We derived a Formula For this quantity, u e = 1 2 ε 0 E 2 (iF there are no dielectric materials). This Formula applies to both electrostatic and induced E-felds. We also saw that magnetic felds possess energy, and we Found a Formula For the magnetic energy density u m = B 2 /2 μ 0 . IF there are both electric and magnetic felds, the total electromagnetic energy density is the sum oF u e and u m . These speciFy at any time oF how much electromagnetic feld energy there is at any point. But we have not yet considered how this energy moves From place to place. Take For example the energy ±ow in a simple DC circuit consisting oF a battery and a resistor. We know that electromagnetic energy moves From the battery to the resistor, where it is converted into thermal energy. It is tempting to assume that the energy ±ows through the wires oF the circuit, like water in a pipe. But iF we look careFully we fnd that the energy density in the wires is much too small to account For the amount oF energy in transit. In Fact nearly all oF the energy gets to the resistor by ±owing through the space around the wires. In a sense the wires guide the energy but do not carry it. OF course the ±ow oF energy in electromagnetic waves such as light is not guided by any wires, let alone carried by them. Clearly we need to understand better the nature oF this kind oF energy ±ow. Energy fow in the Felds In describing any ±ow oF energy through space, it is useFul to talk in terms oF the power crossing unit area perpendicular to the ±ow. This is the intensity , usually denoted by I . PHY 54 1 Electromagnetic Energy

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Intensity Intensity is the amount of power crossing unit area perpendicular to the direction of the Fow. Intensity is simply related to the energy density u and the speed of Fow v : I = uv This is a general relation, not speci±c to electromagnetic energy. ²or electromagnetic ±elds, the energy density (in empty space) is u tot = u e + u m = 1 2 ε 0 E 2 + B 2 μ 0 , and the speed of Fow is c , the speed of light. Around 1900 an important insight was gained in a theorem proved by Poynting, relating the various aspects of energy Fow in electromagnetism. To describe this Fow he introduced a new quantity, now called the Poynting vector : Poynting vector S = E × B 0 Consider a region of space surrounded by a closed surface. Within this surface can be anything (charges, circuits, batteries, resistors, generators, motors, etc.). The total
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## This note was uploaded on 10/19/2011 for the course PHYSICS 54L taught by Professor Thomas during the Summer '09 term at Duke.

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energy - Physics 54 Electromagnetic Energy We all get...

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