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## Homework Statement

A small magnetic moment [tex]\vec{m}(t)[/tex] fixed at position [tex]\vec{r}[/tex] varies in a complicated way as a function of time.

(a) Show that if the time variation is "slow enough", the voltage generated around an arbitrary loop of wire near the origin is

[tex]E(t)=\alpha \frac{\vec{B}_{test}(\vec{r})}{I_{test}}\cdot \frac{d\vec{m}}{dt}[/tex]

and determine the coefficient [tex]\alpha[/tex]. Here, [tex]\vec{B}_{test}(\vec{r})[/tex] is the magnetic field due to a "fictitious test current" [tex]I_{test}[/tex] flowing in the wire. This field is evaluated at the position of the magnetic moment. State your result in terms of the voltage generated by integrating around the loop in the direction of the test current.

(b) Define what is meant by "slow enough"

**2. The attempt at a solution**

I have tried figuring out how to go about calculating the magnetic flux through an "arbitrary loop". But I am a little lost on how to incorporate the test current and test magnetic field into it.

Any input on this would be much appreciated.