L12.4 Ampere’s law
Use Ampere’s law to describe the magnetic field created by a moving charge carrier.
Ampere’s law relates the magnitude of the magnetic field to the current enclosed by a closed imaginary path called an Amperian loop. \[\begin{equation} \oint \vec{B}\cdot d\vec{l} = \mu_0 I_{enc} \end{equation}\]
Ampere’s law can be used to determine the magnetic field near a long, straight current carrying wire. \[\begin{equation} B_{\text{wire}} = \dfrac{\mu_0}{2\pi} \dfrac{I}{r} \end{equation}\]
Unless otherwise stated, all solenoids are assumed to be very long, with uniform magnetic fields inside the solenoids and negligible magnetic fields outside the solenoids.
Ampere’s law can be used to determine the magnetic field inside of a long solenoid. \[\begin{equation} B_{\text{sol}} = \mu_0 n I \end{equation}\]
An Amperian loop is a closed path around a current-carryingconductor.
The principle of superposition can be used to determine the net magnetic field at a point in space created by various combinations of current-carrying conductors, or conducting loops, segments, or cylinders.
Maxwell’s equations are the collection of equations that fully describe electromagnetism. Maxwell’s fourth equation is Ampere’s law with Maxwell’s addition; it states that magnetic fields can be generated by electric current (Ampere’s law) and that a changing electric field creates a magnetic field, similar tot he way a moving charge creates a magnetic field (Maxwell’s addition).
\[\begin{equation} \oint \vec{B} \cdot d\vec{l} = \mu_0 I + \mu_0 \epsilon_0 \dfrac{d \Phi_E}{dt} \end{equation}\]
See also
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