Ampere’s Law

Section 28.1 Ampere’s Law

Video Lesson 28.1.1. Ampere’s Law.

Subsubsection Key Ideas

Definition 28.1.2. Ampere’s Law.

Ampere’s Law relates the net magnetic field around a closed curve to the current passing through the region bounded by the curve:

\begin{equation*} \bigcirc \!\!\!\!\!\!\!\!\int_S \vec{B}\cdot d\vec{s} = \mu_o I_{enclosed} \end{equation*}

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The integral in the definition above is a line integral. The circle over the integral symbol indicates that this is an integral over a closed path. Ampere’s Law is useful when you are able to identify a symmetry of your current distribution.

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Subsubsection Activities

Explanation 28.1.1. Three Loops.

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Shown below are three different cases, each with two identical current-carrying wires and a circular Amperian loop. In which case is the net magnetic field around the loop the largest?

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Three boxes sit side by side. The lefthand box is case A, where one wire sits inside a closed Amperian loop and another wire sits outside the loop. The middle box shows case B, where both wires sit outside the loop. The righthand box shows case C where both wires sit inside the loop. — Figure 28.1.3. Three cases are shown depicting an Amperian loop (dashed line) and different wires.
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