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Unformatted text preview: 1 Lecture 22 Chapter 22. Patterns of Field in Space Gauss’ Law for Magnetism Ampere’s Law Divergence ˆ ε ∑ ∑ = Δ ⋅ inside surface q A n E ∫ ∑ = ⋅ ˆ ε inside q dA n E 2 4 1 r Q E πε = Gauss’ Law Gauss’s 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 Gauss’s 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 Ampère’s Law B i d l = μ 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 = μ o I inside _ path ∑ ∫ Can B have an out of plane component?...
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 Spring '07
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 Law, Magnetism, Work, Magnetic Field

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