- #1

Graham87

- 63

- 16

- Homework Statement
- See pictures

- Relevant Equations
- See pictures

A current current loop is running through this figure.

How do I design integration surfaces to find the magnetic dipole moment?

In the solution the three following figures were designed for integration surface, and they prove that they all give the same answer of ## m= 2IRd \hat{z} ##.

For a) they just did the area of the rectangle which is 2Rd for the vector area, since the sides cancel. Shouldnt one need to calculate the area for the top surface of the integration surface?

For b) they did it this way:

For c) they similarly

My problem is I do not understand how to go about finding integration surfaces. What are they for? What are the criterias? How do they work?

So the vector area of the magnetic dipole moment is not the area enclosed in the current loop?

Why do they only find the area of the top surface in b) while neglecting the top surface in a)?

Im not sure how this works mathematically. Is there anything to do with boundary surface? How come one does not calculate the boundary surface?

Thanks

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