Lecture_22_Part_2

Lecture_22_Part_2 - Flux through small area: A n E flux !...

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Unformatted text preview: Flux through small area: A n E flux ! " ~ r Definition of electric flux on a surface: ! " # surface A n E r Electric Flux ! " # surface A n E r ! " dA n E r A d r ! " A d E r r electric flux on a closed surface = r E ! d r A " ! " " = # $ inside surface q A n E r ! " = # $ inside q dA n E r 2 4 1 r Q E !" = Gausss Law Gausss law: If we know the field distribution on closed surface we can tell what is inside. 1. Knowing E can conclude what is inside 2. Knowing charges inside can conclude what is E Can derive one from another Gausss law is more universal: works at relativistic speeds Dipoles: Electric field: + and charges can be separated Magnetic field: no monopoles Suppose magnetic dipole consists of two magnetic monopoles, each producing a magnetic field similar to the electric field. One cannot separate them total magnetic charge is zero. ! " " = # $ inside surface q A n E r Gausss law for magnetism = ! " # surface A n B r = ! " # A n B r or Gausss Law for Magnetism All the currents in the universe contribute to B but only the ones inside the path result in nonzero path integral Amperes law is almost equivalent to the Biot-Savart law: but Amperes law is relativistically correct Ampres Law ! " = # path inside I l d B _ r r 1. Choose the closed path 2. Imagine surface (soap film) over the path ! " l d B r r 3. Walk counterclockwise around the path adding up 4. Count upward currents as positive, inward going as negative !...
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Lecture_22_Part_2 - Flux through small area: A n E flux !...

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