Magnetic Field of a Solenoid Step 1 Cut
- Slides: 17
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: B Number of loops per meter: N/L Number of loops in z: (N/L) z Field due to z:
Magnetic Field of a Solenoid Step 3: Add up the contribution of all the pieces B Magnetic field of a solenoid:
Magnetic Field of a Solenoid Special case: R<<L, center of the solenoid: in the middle of a long solenoid
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?
Helmholtz Coils How what is B near the origin? Assume that the positions of the loops are large compared to their radii.
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 Curly character – introduce: Similar to Gauss’s law (Q/ 0) Will it work for any circular path of radius r ?
A Noncircular Path Need to compare and Where in loop doesn’t matter!
Currents Outside the Path Need to compare and for currents outside the path
Three Current-Carrying Wires Ampere’s law
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
Inside the Path Ampere’s law 1. 2. 3. 4. Choose the closed path Imagine surface (‘soap film’) over the path Walk counterclockwise around the path adding up Count upward currents as positive, inward going as negative
What is ?
Ampere’s Law: A Long Thick Wire Can B have an out of plane component? Is it always parallel to the path? for thick wire: (the same as for thin wire) Would be hard to derive using Biot-Savart law
Ampere’s Law: A Solenoid Number of wires: (N/L)d What is on sides? B outside is very small (solenoid) Uniform: same B no matter where is the path
Ampere’s Law: A Toroid Symmetry: B || path Is magnetic field constant across the toroid?
- Magnetic field solenoid
- Magnetic field in solenoid
- Step 1 step 2 step 3 step 4
- Force on charged particle
- Magnetic moment and magnetic field relation
- Magnetic flux units
- 21lwuy8i6hw -site:youtube.com
- Distinguish between magnetic and nonmagnetic materials
- Magnetic field
- Induced electric field of a solenoid
- Crosscut vs rip saw
- Define consistent cut
- Example of a cutaway shot
- Prolog green vs red cut
- Difference between magnetic flux and magnetic flux density
- Horseshoe magnet magnetic field
- Multipole expansion of magnetic vector potential
- When a charged particle moves in a region of magnetic field