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Magnetic Field of a Solenoid

B. Magnetic Field of a Solenoid. Step 1: Cut up the distribution into pieces. Step 2: Contribution of one piece. origin: center of the solenoid. one loop:. Number of loops per meter: N/L. Number of loops in  z : ( N/L )  z. Field due to  z :. B. Magnetic Field of a Solenoid.

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Magnetic Field of a Solenoid

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  1. B Magnetic Field of a Solenoid Step 1:Cut up the distribution into pieces Step 2:Contribution of one piece origin:center of the solenoid one loop: Number of loops per meter:N/L Number of loops in z: (N/L) z Field due to z:

  2. B Magnetic Field of a Solenoid Step 3:Add up the contribution of all the pieces Magnetic field of a solenoid:

  3. Magnetic Field of a Solenoid Special case: R<<L, center of the solenoid: in the middle of a long solenoid

  4. Triangular coil There is a current going through a triangular coil. Which direction is B at the center? How would you find the magnitude of B?

  5. Helmholtz Coils There is a current going through the two identical loops producing a magnetic dipole moment of in each loop. Which direction is B on the x-axis? How what is B near the origin? Assume that the positions of the loops are large compared to their radii.

  6. 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

  7. 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 ?

  8. Need to compare and A Noncircular Path Where in loop doesn’t matter!

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

  10. Ampere’s law Three Current-Carrying Wires

  11. 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

  12. 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

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

  14. What is I ? • A • A • A • A

  15. 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

  16. 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

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

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