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Question 5.7: Find the magnetic field a distance s from a long straight wi...

Find the magnetic field a distance s from a long straight wire (Fig. 5.32), carrying a steady current I (the same problem we solved in Ex. 5.5, using the Biot-Savart law).

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We know the direction of B is “circumferential,” circling around the wire as indicated by the right-hand rule. By symmetry, the magnitude of B is constant around an Amperian loop of radius s, centered on the wire. So Ampère’s law gives

\oint{\pmb{B}.dI}=B\oint{dl}=B2\pi s =\mu _{0}I_{enc}=\mu _{0}I,

or

B=\frac{\mu _{0}I}{2\pi s}.

This is the same answer we got before (Eq. 5.38), but it was obtained this time
with far less effort.

B=\frac{\mu _{0}I}{2\pi s}.       (5.38)

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