Ampere’s Law

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Section 28.1 Ampere’s Law

Definition 28.1.1. 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*}

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.

Exercises Activities

1.

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?

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 28.1.2. Three cases are shown depicting an Amperian loop (dashed line) and different wires.

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