The Biot-Savart law describes the magnetic field generated by a steady electric current. It states that the magnetic field at a point in space is proportional to the current element and inversely proportional to the square of the distance from the element.
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The Biot-Savart law formula is given by $$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \hat{r}}{r^2}$$ where $I$ is the current, $d\mathbf{l}$ is the length vector, $\hat{r}$ is the unit vector from the current element to the point of interest, and $r$ is the distance.
It can be used to calculate the magnetic field produced by currents in various configurations such as straight wires, loops, and solenoids.
The Biot-Savart law applies only to steady (constant) currents and does not account for time-varying electromagnetic fields.
It is derived from Ampere's Law but provides a more direct way to compute magnetic fields for arbitrary current distributions.
In practical applications, it often requires integration over a continuous distribution of current elements.
Review Questions
What is the fundamental equation of the Biot-Savart law?
How does distance affect the magnetic field according to the Biot-Savart law?
For what types of currents is the Biot-Savart law applicable?
A fundamental law stating that for any closed loop path, the sum of length elements times their magnetic field in that direction equals $\mu_0$ times the electric current enclosed in that loop.