Ampère's Law The French physicist André-Marie Ampère

QUESTION:

Ampere's Law The French physicist André-Marie Ampere (1775-1836) discovered that an electrical current I in a wire produces a magnetic field B. A special case of Ampérels Law relates the current to the magnetic field through the equation \(\oint_{C} \mathbf{B} \cdot d \mathbf{r}=\mu I\). where C is any closed curve through which the wire passes and p. is a physical constant. Assume that the current I is given in terms of the current density .I as \(I=\iint_{S} \mathbf{J} \cdot \mathbf{n} d S\). where S is an oriented surface with C as a boundary. Use Stokes' Theorem to show that an equivalent form of Ampere's Law is \(\nabla \times \mathbf{B}=\mu \mathbf{J}\).

Text Transcription:

oint_C B cdot dr = mu l

I = iint_S J cdot n dS

Nabla x B = muJ