E&M - flux encircled by orbit of particles is conserved

In summary, the flux encircled by the orbit of particles in a magnetic mirror is conserved even when the magnetic field varies. This is due to the fact that the flux is represented as BA for circular orbits, where A is the area of a circle and R is the radius. By relating R to the value of the B-field and rescaling B to B'=aB, it can be shown that the flux remains constant regardless of the value of "a".
  • #1
Qyzren
44
0
Prove that in a magnetic mirror the flux encircled by the orbit of the particles is conserved when the magnetic field varies.

How do you do this? i have no idea how to approach/start this!
 
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  • #2
The flux is BA for the circular orbits (as you change the direction of the B field, the orbits adjust direction so that the flux is clearly the same) where A=area for a circle, found from the radius R. You can relate the radius R to the value of the B-field (and other quantities). Rescale B to B'=aB everywhere in your equations and show that the flux is independent of "a".
 

1. What is flux encircled by orbit of particles?

The flux encircled by orbit of particles refers to the amount of electric or magnetic field lines passing through a closed loop or orbit of charged particles. It is a measure of the strength of the field within the loop or orbit.

2. Why is flux encircled by orbit of particles conserved?

Flux encircled by orbit of particles is conserved because according to Faraday's Law, a changing magnetic flux induces an electric field, which in turn creates a current in the loop of particles. This current produces its own magnetic field that opposes the original change in flux, thus conserving the total flux.

3. How is the conservation of flux encircled by orbit of particles related to electromagnetic induction?

The conservation of flux encircled by orbit of particles is directly related to electromagnetic induction. This is because, as mentioned before, a changing magnetic flux induces an electric field, and vice versa, an electric field can induce a magnetic field. This phenomenon is the basis of electromagnetic induction, which is the process of generating an electric current by changing the magnetic flux through a loop of wire.

4. Can the flux encircled by orbit of particles be affected by external factors?

Yes, the flux encircled by orbit of particles can be affected by external factors such as the strength of the magnetic field, the size and shape of the loop, and the speed of the particles. Any changes in these factors can result in a change in the total flux encircled by the orbit of particles.

5. How is the conservation of flux encircled by orbit of particles used in practical applications?

The conservation of flux encircled by orbit of particles is used in various practical applications, such as electric generators and motors, transformers, and induction cooktops. These devices utilize the principle of electromagnetic induction to convert mechanical energy into electrical energy or vice versa, and the conservation of flux is essential for their proper functioning.

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