- #1
center o bass
- 560
- 2
Hello, calculating the magnetic moment of a current loop is trivial, but I want to do it with the general formula
[tex]\vec m = \frac{1}2 \int \vec r \times \vec J(\vec r) d^3\vec r[/tex]
The only thing which is stopping me is to find a good argument on why
[tex]\frac{1}{2}\int \vec r d\vec r = \vec A[/tex] where [tex]\vec A[/tex] is the area vector of the loop. Is there a formal way of proving this or any intuitive diagrams one can draw to show that it must be true.
[tex]\vec m = \frac{1}2 \int \vec r \times \vec J(\vec r) d^3\vec r[/tex]
The only thing which is stopping me is to find a good argument on why
[tex]\frac{1}{2}\int \vec r d\vec r = \vec A[/tex] where [tex]\vec A[/tex] is the area vector of the loop. Is there a formal way of proving this or any intuitive diagrams one can draw to show that it must be true.