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Patterns of Magnetic Field in Space

Patterns of Magnetic Field in Space. Is there current passing through these regions?. There must be a relationship between the measurements of the magnetic field along a closed path and current flowing through the enclosed area. Ampere’s law. Quantifying the Magnetic Field Pattern.

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Patterns of Magnetic Field in Space

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  1. Patterns of Magnetic Field in Space Is there current passing through these regions? There must be a relationship between the measurements of the magnetic field along a closed path and current flowing through the enclosed area. Ampere’s law

  2. Quantifying the Magnetic Field Pattern Curly character – introduce: Similar to Gauss’s law (Q/0) Will it work for any circular path of radius r ?

  3. Need to compare and A Noncircular Path

  4. Need to compare and Currents Outside the Path for currents outside the path

  5. Ampere’s law Three Current-Carrying Wires

  6. Ampère’s Law All the currents in the universe contribute to B but only ones inside the path result in nonzero path integral Ampere’s law is almost equivalent to the Biot-Savart law: but Ampere’s law is relativistically correct Ampere, 1826: Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience

  7. 3. Walk counterclockwise around the path adding up Ampere’s law Inside the Path • Choose the closed path • Imagine surface (‘soap film’) over the path 4. Count upward currents as positive, inward going as negative

  8. for thick wire: (the same as for thin wire) Ampere’s Law: A Long Thick Wire Can B have an out of plane component? Is it always parallel to the path? Would be hard to derive using Biot-Savart law

  9. What is on sides? (solenoid) Ampere’s Law: A Solenoid Number of wires: (N/L)d B outside is very small Uniform: same B no matter where is the path

  10. Ampere’s Law: A Toroid Symmetry:B || path Is magnetic field constant across the toroid?

  11. What is I ? • A • A • A • A

  12. , , w=0.5m, h=0.2m, What is ? What is ? = .866 0 Tm 8.7Tm 1.7 Tm 2.0 Tm 2.1 Tm

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