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Illustration Position Vectors for the Biot-Savart Law for a thin Wire

Position Vectors for the Biot-Savart Law for a thin Wire
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An arbitrarily shaped, thin wire through which an electric current \(I\) flows. The position vector \(\boldsymbol{R}\) points to the infinitesimal line element\(\text{d}\boldsymbol{s}\) along the wire. The position vector \(\boldsymbol{r}\) on the other hand, points to the field point where the magnetic field \(\boldsymbol{B}(\boldsymbol{r})\) needs to be calculated with the Biot-Savart law. The connecting vector \(\boldsymbol{r} - \boldsymbol{R} \) points from the line element to the field point.