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Unformatted text preview: 1 Lecture 22 Chapter 22. Patterns of Field in Space Gauss Law for Magnetism Amperes Law Divergence = inside surface q A n E = inside q dA n E 2 4 1 r Q E = Gauss 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 4/10/11 3 Gauss Law for Magnetism Since all lines of B are closed loops, any B line leaving a closed surface MUST reenter it somewhere. TRUE IN GENERAL, not just for this dipole example A B B All the currents in the universe contribute to B but only the ones inside the path result in nonzero path integral Ampres Law B i d l = o I inside _ path 2 l d B 3. Walk counterclockwise around the path adding up 1. Choose the closed path 2. Imagine surface (soap film) over the path 4. Count upward currents as positive, inward going as negative Inside the Path B i d l = o I inside _ path Can B have an out of plane component?...
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