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Illustration Integration Path Around a Current-Carrying Coil

Integration path for the magnetic field of a long coil
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Selected rectangular integration path (rectangular loop) around a current-carrying coil to use Ampere's law to calculate the magnetic field inside the coil. The rectangular loop is composed of four integration paths: \(\mathcal{S}_1\), \(\mathcal{S}_2\), \(\mathcal{S}_3\) and \(\mathcal{S}_4\).

The loop is 'punctured' by the current \(N\) times.