Moving magnetic dipole into current loop

Click For Summary
SUMMARY

The discussion focuses on the problem of determining the induced current in a perfectly conducting circular loop when a magnetic dipole is moved to a specific position along its axis. The magnetic dipole, denoted as m, induces a current I in the loop due to the changing magnetic field as it approaches the loop. The self-inductance of the loop is represented by L, and the relationship between magnetic flux and current is established through the equation Φ = LI. The final position of the dipole, located a distance z from the center of the loop, is critical for calculating both the induced current and the force between the dipole and the loop.

PREREQUISITES
  • Understanding of magnetic dipoles and their properties
  • Familiarity with self-inductance and its implications in circuits
  • Knowledge of vector potential in electromagnetic theory
  • Basic principles of electromagnetism, particularly Faraday's law of induction
NEXT STEPS
  • Study the derivation of the vector potential for a magnetic dipole
  • Learn about the mathematical formulation of induced currents in loops
  • Explore the concept of magnetic flux and its calculation in electromagnetic systems
  • Investigate the forces between magnetic dipoles and conductive loops in detail
USEFUL FOR

This discussion is beneficial for physics students, electromagnetism researchers, and engineers working with magnetic systems and inductive components.

azupol
Messages
17
Reaction score
0

Homework Statement


A magnetic dipole m is moved from infinitely far away to a point on the axis of a fixed, perfectly conducting (zero resistance) circular loop of radius a and self-inductance L. In its final position the dipole is oriented along the axis of the loop and is a distance z from its centre. If the current in the loop is initially zero (i.e. when the dipole is infinitely far away):
a) Find the current in the loop when the dipole is in its final position
b) Calculate the force between the loop and the dipole (in its final position).

Homework Equations


Vector potential of the dipole
Magnetic flux is LI, L is the self-inductance and I is the current

The Attempt at a Solution


I'm not sure how to start this problem. Conceptually, I think that moving in the dipole from infinity will induce a current in the loop due to the changing magnetic field, but I can't come up with a rigorous argument.
 
Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Similar threads

On the magnetic dipole radiation in Griffith's book
  • · Replies 1 ·
Replies
1
Views
2K
Electric Dipole Radiation from a Spinning Current Loop
  • · Replies 1 ·
Replies
1
Views
3K
Why is a current ring approx a magnetic dipole from very far off?
  • · Replies 7 ·
Replies
7
Views
2K
Question regarding current loops - electric dipole radiation
  • · Replies 6 ·
Replies
6
Views
2K
Understanding work in translation and rotation of a magnetic dipole
  • · Replies 1 ·
Replies
1
Views
2K
Deriving magnetic dipole moment from multipole expansion
  • · Replies 1 ·
Replies
1
Views
3K
Effect of different magnetic fields on a magnetic dipole
  • · Replies 25 ·
Replies
25
Views
2K
Magnetic field of a semi infinite sheet of current
  • · Replies 3 ·
Replies
3
Views
2K
Vector Potential of a Rotating Mangetic Dipole
  • · Replies 5 ·
Replies
5
Views
4K
How to calculate the dipole moment of the spherical shell?
  • · Replies 1 ·
Replies
1
Views
8K