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# Experiments show that a steady current $I$ in a long wire produces a magnetic field $\textbf{B}$ that is tangent to any circle that lies in the plane perpendicular to the wire and whose center is the axis of the wire (as in the figure). $\textit{Ampere's Law}$ relates the electric

## \begin{aligned} \int_{C} \mathbf{B} \cdot d \mathbf{r} &=2 \pi r B=\mu_{0} I \\ B &=\frac{\mu_{0} I}{2 \pi r} \end{aligned}

Vector Calculus

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So the power is not complete here on the If you look at the text book, you have a complete description of the proper them and and the picture. So basically, the idea is this You have this and peace. Ah, come on. I mean, peace. That meant that you feel which can be computed by this. So fix it, fix our radius. Is this wise given? So is there is nothing special. You can use these two qualities to verify that this isn't true because this is simply I've is constant than Hume ut pride visor that does the lands up the curve, which is which is self. The curve is a radius our circle. So the lens or the so home expenses two pi r And when you use private together, you have museum tough guy. That's art museum time side. And that's basically it's kind of a mathematical explanation. Off, sir. Off the physics role. So impersonal

#### Topics

Vector Calculus

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp