L12.3 Magnetic fields of current-carrying wires and the Biot-Savart law
Describte the magnetic field produced by a current carrying wire.
The Biot-Savart law defines the magnitude and direction of a magnetic field created by an electrical current. \[\begin{equation} d\vec{B} = \dfrac{\mu_0}{4\pi} \dfrac{I(d\vec{l} \times \hat{r}}{r^2} \end{equation}\]
The magnetic field vectors around a small segment of a current-carrying wire are tangent to concentric circles centered on that wire. The field has no component toward, away fromm, or parllel to the segment of the current-carrying wire.
The Biot-Savart law can be used to derive the magnitudes and directions of magnetic fields around segments of current-carrying wires, for example at the center of a circular loop of wire. \[\begin{equation} B_{\text{center of loop}}= \dfrac{\mu_0 I}{2R} \end{equation}\]
Describe the force exerted on current-carrying wires by a magnetic field
A magnetic field will exert a force on a current carrying wire. \[\begin{equation} \vec{F}_{B} = \int I \int(d\vec{l} \times \vec{B}) \end{equation}\]
See also
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