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Sources of the Magnetic Field

When we introduced the electric field $\vec{E}$ it was apparent that electric charges were the source of such a field. Experiments in the 19th century showed that the source of a magnetic field $\vec{B}$ was a moving charge, or current. A detailed mathematical relation between a charge moving at velocity $\vec{v}$ and the associated magnetic field $\vec{B}$ is known as Ampère's law or, in another form, the Biot-Savart law. We will consider three special cases of the results of this law.