Lecture_10_(Chap.18)

# Lecture_10_(Chap.18) - Energy Density of Electric Field...

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Energy Density of Electric Field Energy can be stored in electric fields E Q / A (for small s ) one _ plate 2 0 F ( Q / A ) by _ you Q Q 2 0 U electric F by _ you s Q ( Q / A ) s s A A Q U el 2 0 / 1 olume 2 0 0 2 E volume U el 1 E 2 ieldenergydensity: /m 3 volume 2 0 Field energy density: (J/m ) Energy expended by us was converted into energy stored in the electric field 1

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Energy Density of Electric Field the previous slide the “system” is the set of two plates Work In the previous slide, the system is the set of two plates. Work, W external > 0, is done on the system by you – part of the “surroundings.” E system   KE   U electric W external If the force exerted by you just offsets the attractive force, F by-plates , so that the plate moves with no gain in KE, U electric W external F by _ you s 2
Potential Energy and Field Energy In a multiparticle system we can either consider a change in potential energy or a change in field energy ( but not both ); the quantities are equal. The idea of energy stored in fields is a general one: Magnetic and gravitational fields can also carry energy. The concept of energy stored in the field is very useful: - electromagnetic waves 3

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An Electron and a Positron System Surroundings e + e - Release electron and positron – the electron (system) will gain kinetic energy Conservation of energy surrounding energy must decrease Does the energy of the positron decrease? - No, it increases Where is the decrease of the energy in the surroundings? - Energy stored in the fields must decrease 4
An Electron and a Positron System Surroundings e + e - Single charge: 1 Energy: V 2 1 2 r Dipole: dV E 0 2 3 1 ~ r E (far) Energy stored in the E fields decreases as e + and e - get closer! 5

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An Electron and a Positron System Surroundings e + e - i i l f t i f (Field energy) + K positron + K electron = 0 Principle of conservation of energy: (Field energy) = -2( K electron ) Alternative way: e + and e - are both in the system: U el = -2( K electron ) Change in potential energy for the two-particle system is the same as the change in the field energy 6
Chapter 18 Magnetic Field 7

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Lecture_10_(Chap.18) - Energy Density of Electric Field...

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