Moving magnetic dipole into current loop

In summary, the problem involves a magnetic dipole being moved from infinity to a point on the axis of a fixed, perfectly conducting circular loop. The final position of the dipole is oriented along the axis of the loop and a distance z from its centre. The current in the loop is initially zero. The problem requires finding the current in the loop and the force between the loop and the dipole in its final position. The relevant equations are the vector potential of the dipole and the magnetic flux, which is equal to the product of self-inductance and current. The concept of induction is important in solving this problem.
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azupol
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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.
 
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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?
 

Related to Moving magnetic dipole into current loop

1. What is a moving magnetic dipole?

A moving magnetic dipole is a magnetic object, such as a magnet or a wire carrying an electric current, that has a magnetic field and is in motion.

2. How does a moving magnetic dipole interact with a current loop?

A moving magnetic dipole can induce an electric current in a nearby current loop, or a current loop can experience a force when placed in a magnetic field created by the moving magnetic dipole.

3. What is the significance of the direction of motion of a magnetic dipole in relation to a current loop?

The direction of motion of a magnetic dipole in relation to a current loop determines the direction of the induced current or the direction of the force experienced by the loop. This is governed by the right-hand rule, where the direction of the current or force is perpendicular to both the direction of the magnetic field and the direction of motion.

4. How does the strength of the magnetic dipole or current loop affect their interaction?

The strength of the magnetic dipole or current loop affects the magnitude of the induced current or the force experienced. The stronger the magnetic dipole or current loop, the greater the effect on each other.

5. What are some real-world applications of moving magnetic dipoles and current loops?

Moving magnetic dipoles and current loops have many practical applications, such as in generators, motors, transformers, and magnetic levitation systems. They are also used in scientific research, such as in magnetic resonance imaging (MRI) machines.

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