# Derivation for Magnetic Dipole of Current Loop

• newbie101
In summary, a user is asking for a derivation of the vector potential A for a magnetic dipole, specifically from equation 8.21 to 8.21a. They have tried all day to obtain it but have had no luck and need it explained step by step. The user also asks for help in obtaining the distance p and vector A. Another user provides a link to a page with the solution and reminds the user that the magnetic potential is the solution of Poisson's equation for magnetostatics. Another user points out that the solution involves the cosine law in a triangle. Finally, a user asks for a soft copy of the derivation but is reminded that the thread is from 2005.
newbie101
Hi All,

Please show me the derivation of the vector potentiol A for the magnetic dipole.
from equation 8.21 to 8.21a

** i tried all day and couldn't manage to obtain it. i need the derivation step by step **

thanks
newbie

http://img.photobucket.com/albums/v712/newbie777/MagneticDipole.jpg

Last edited by a moderator:
Thanks Doc

It looks like the cosine law in a triangle.You should spot that triangle out from the drawing (check all slides).

And the magnetic potential is the solution of Poisson equation for magnetostatcs.

Daniel.

gawd.. how could i miss that

hi can i get the derivation(soft copy), newbie101?

Please note that you're asking for something in a thread that was last active on May 3rd, 2005.

Zz.

## 1. What is the magnetic dipole moment of a current loop?

The magnetic dipole moment of a current loop is a measure of the strength and direction of the magnetic field produced by the loop. It is defined as the product of the current in the loop, the area enclosed by the loop, and the unit vector perpendicular to the loop's plane.

## 2. How is the magnetic dipole moment of a current loop derived?

The magnetic dipole moment of a current loop can be derived using the Biot-Savart law, which relates the magnetic field at a point to the current and distance from the point to the current element. By integrating this law over the entire loop, the magnetic dipole moment can be calculated.

## 3. What is the direction of the magnetic dipole moment of a current loop?

The direction of the magnetic dipole moment of a current loop is determined by the right-hand rule. If your right thumb points in the direction of the current, then your curled fingers will point in the direction of the magnetic dipole moment.

## 4. How does the magnetic dipole moment of a current loop change with different loop geometries?

The magnetic dipole moment of a current loop is directly proportional to the area enclosed by the loop. This means that changing the size or shape of the loop will change the magnetic dipole moment. Additionally, the direction of the magnetic dipole moment can also be affected by the orientation of the loop in relation to the current flow.

## 5. What are some applications of the magnetic dipole moment of a current loop?

The magnetic dipole moment of a current loop has important applications in electromagnetism, such as in the design of electromagnets and electric motors. It is also used in magnetic resonance imaging (MRI) technology, which utilizes the magnetic dipole moment of hydrogen atoms in the body to produce images. Additionally, the magnetic dipole moment is used in studying the Earth's magnetic field and its interactions with the Sun.

• Introductory Physics Homework Help
Replies
7
Views
325
• Introductory Physics Homework Help
Replies
1
Views
460
Replies
1
Views
1K
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
205
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
25
Views
352
• Introductory Physics Homework Help
Replies
3
Views
311