Electromagnetic-Fields-and-Waves

# Electromagnetic-Fields-and-Waves - Electromagnetic Fields...

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Electromagnetic Fields and Waves

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E or B? It Depends on Your Perspective Charges create an electric field Moving charges create a magnetic field. Is there ? B The force as measured by Bill B v q F × = The force as measured by Sharon 0 F = Velocity relative to what?
Galilean Relativity Consider two reference frames with constant velocity with respect to each other V ' v v or V v ' v + = - = dt V d dt v d dt ' v d - = F ' F a ' a = =

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The Transformation of Electric and Magnetic Fields,1 Imagine that Bill has measured the electric field and magnetic field in frame S. Bill has established a region of space in which there is a uniform magnetic field but no electric field. The net force on the charge is But Sharon in S’ sees a stationary charge with an upward force. Her conclusion is there must be an upward electric field B v q B v q E q F × = × + = B V ' E × =
The Transformation of Electric and Magnetic Fields,2 Whether a field is seen as “electric” or “magnetic” depends on the motion of the reference frame relative to the sources of the field. In general, if an experimenter in S creates both an electric field and magnetic field. The Lorentz force on a charge q is ( 29 B V E ' E B v E q F × + = × + =

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Transformation of Electric and Magnetic Fields,3 Consider a charge q at rest in frame S. Coulomb’s law is still valid in a frame in which the charge is moving. The magnetic field of a moving charge is given by Biot-Savart law The Biot-Savart law for the magnetic field of a moving point charge is nothing other than the Coulomb electric field of a stationary point charge transformed into a moving reference frame. In general, r ˆ r q 4 1 E ' E 2 0 πε = = E V r ˆ ' v r q 4 ' B 0 0 2 0 × - = × = μ ε π E V B ' B 0 0 × - =
Galilean Field Transformation where V is the velocity of frame S

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## This note was uploaded on 04/02/2012 for the course PHYSICS 270 taught by Professor Drake during the Spring '08 term at Maryland.

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Electromagnetic-Fields-and-Waves - Electromagnetic Fields...

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