Then this current produces a Magnetic Field which circles the wire. The left side of Equation [2] means: If you take any imaginary path that encircles the wire, and you add up the Magnetic Field at each point along that path, then it will numerically equal the amount of current that is encircled by this path which is why we write for encircled or enclosed current. Suppose we have a long wire carrying a constant electric current, I [Amps]. What is the magnetic field around the wire, for any distance r [meters] from the wire? We have a long wire carrying a current of I Amps. We want to know what the Magnetic Field is at a distance r from the wire.

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The direction of the normal must correspond with the orientation of C by the right hand rule , see below for further explanation of the curve C and surface S. Ambiguities and sign conventions[ edit ] There are a number of ambiguities in the above definitions that require clarification and a choice of convention. These ambiguities are resolved by the right-hand rule : With the palm of the right-hand toward the area of integration, and the index-finger pointing along the direction of line-integration, the outstretched thumb points in the direction that must be chosen for the vector area dS.

Also the current passing in the same direction as dS must be counted as positive. The right hand grip rule can also be used to determine the signs. Second, there are infinitely many possible surfaces S that have the curve C as their border. Imagine a soap film on a wire loop, which can be deformed by moving the wire. Which of those surfaces is to be chosen?

If the loop does not lie in a single plane, for example, there is no one obvious choice. In practice, one usually chooses the most convenient surface with the given boundary to integrate over. Free current versus bound current[ edit ] The electric current that arises in the simplest textbook situations would be classified as "free current"—for example, the current that passes through a wire or battery.

All materials can to some extent. When a material is magnetized for example, by placing it in an external magnetic field , the electrons remain bound to their respective atoms, but behave as if they were orbiting the nucleus in a particular direction, creating a microscopic current. When the currents from all these atoms are put together, they create the same effect as a macroscopic current, circulating perpetually around the magnetized object.

This magnetization current JM is one contribution to "bound current". The other source of bound current is bound charge. When an electric field is applied, the positive and negative bound charges can separate over atomic distances in polarizable materials , and when the bound charges move, the polarization changes, creating another contribution to the "bound current", the polarization current JP. The total current density J due to free and bound charges is then: J.


7.4: Ampere’s Circuital Law (Magnetostatics) - Integral Form



Ampere's Law


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