>[!summary] The most general equation to describe magnetic fields through current loops > **Key equations:** > General equation: $dB = \frac{\mu _0 i \space dr \times \hat{r}}{4\pi R^3}$ > Magnetic field of a Current wire: $B = \frac{\mu_0i }{2R}$ # What is Biot-Savart Law Biot-savart law is the most general equation to describe the magnetic field through current loops. This equation can be derived through special relativity but it will not be done in this note. General equation: $\begin{array}{c} dB = \frac{\mu _0 i \space dr \times \hat{r}}{4\pi R^3} \\ B = \int dB \\ \text{Solve for B using this approch} \end{array} $ # Current Example Let's suppose to find the magnetic field around a circular current carrying wire. If you know the radius, current (i) and the end points we can use this general sol $\begin{array}{c} dB = \frac{\mu _0 i \space dr \times r}{4\pi R^2} \\ dB = \frac{\mu _0 i \space d\theta R}{4\pi R^2} \\ \text{Using the arugment to find $d\theta$ because its over a circle} \\ \\ B = \frac{\mu _0i} {4\pi R} \hat{r}\int_0^{2\pi} d\theta \\ B = \frac{\mu_0i }{2R} \end{array}$