Ampère’s Law The French physicist André-Marie Ampère (1775–1836) discovered that an electrical current I in a wire produces a magnetic field B. A special case of Ampère’s Law relates the current to the magnetic field through the equation ∮C B ⋅ dr = μI, where C is any closed curve through which the wire passes and μ is a physical constant. Assume the current I isgiven in terms of the current density J as I = ∫∫S J ⋅ n dS, where Sis an oriented surface with C as a boundary. Use Stokes’ Theoremto show that an equivalent form of Ampère’s Law is ∇ x B = μJ.

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Ampère’s Law The French physicist André-Marie Ampère (1775–1836) discovered that an electrical current I in a wire produces a magnetic field B. A special case of Ampère’s Law relates the current to the magnetic field through the equation ∮C Bdr = μI, where C is any closed curve through which the wire passes and μ is a physical constant. Assume the current I is
given in terms of the current density J as I = ∫∫S J ⋅ n dS, where S
is an oriented surface with C as a boundary. Use Stokes’ Theorem
to show that an equivalent form of Ampère’s Law is x B = μJ.

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