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muppet is offline
Dec27-12, 05:58 PM
P: 590
Ah I see. The equations I'm talking about:
[tex]\mathbf{F}^{ms}(\mathbf{x})=\frac{\mu_0 I I'}{4 \pi} \oint_{C} d\mathbf{l} \times \oint_{C'} \mathbf{l'} \times \frac{\mathbf{x}-\mathbf{x}'}{|\mathbf{x}-\mathbf{x}'|^3} [/tex](1.11)

[tex]d \mathbf{B}^{stat}(\mathbf{x}) \equiv \frac{\mathbf{F}^{ms}(\mathbf{x})}{I} =\frac{\mu_0}{4 \pi} d\mathbf{i}'(\mathbf{x'}) \times \frac{\mathbf{x}-\mathbf{x}'}{|\mathbf{x}-\mathbf{x}'|^3} [/tex] (1.15)
where [itex]d\mathbf{i}(\mathbf{x}')=I d\mathbf{l}' (\mathbf{x'})[/itex]

I'm afraid I still don't understand your answer to 1). Suppose "small" means "small compared to the characteristic scale over which the B-field varies" (which Thide couldn't say at this point). That doesn't make a difference, because the tangent vector to the loop still turns through a complete revolution (!), so no matter how small it is, the corresponding force still pushes different elements in different directions, right?