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Establish a relationship for how the magnetic field of a solenoid varies with distance and current by using both the Biot-Savart law and Ampère’s law; Establish a relationship for how the magnetic field of a toroid varies with distance and current by using Ampère’s law
Quadrupole (Electric or Magnetic): Solenoidal (equations must be interpreted in Larmor Frame: see Appendix B):
12 kwi 2018 · Steps to Derive Equation: 1. Apply Ampere's law by finding the formula for relating the path of the current and magnetic field: ∮ B → • d l →. 2. Find that Ampere's law is proportional to the path and solenoid's length proportionality times the number of turns in the solenoid and the electric current: B l = μ 0 N I l L.
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. The phenomenon is conceptually similar to the precession of a tilted classical gyroscope in an external torque-exerting gravitational field.
Larmor Frequency. When a magnetic moment is placed in a magnetic field it will tend to align with the field. Classically, a magnetic moment can be visualized as a current loop and the influence toward alignment can be described as the torque on the current loop exerted by the magnetic field.
A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. Such coils, called solenoids, have an enormous number of practical applications. The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets. In the above expression for the ...
The magnetic field within a solenoid depends upon the current and density of turns. In order to estimate roughly the force with which a solenoid pulls on ferromagnetic rods placed near it, one can use the change in magnetic field energy as the rod is inserted into the solenoid.
