Magnetic Fields from Currents
Explore how electric currents generate magnetic fields. Drag the orange "Test Point" on the canvas, and adjust the controls to see the magnetic field ($ \vec{B} $) dynamically change!
The Biot-Savart Law ($ d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2} $)
This fundamental law describes the magnetic field ($d\vec{B}$) generated by a small segment of current ($I d\vec{l}$). The field depends on the current's strength and direction, and the distance and orientation to the point where the field is measured. Notice the cross product, indicating the perpendicular nature of the magnetic field.
Ampere's Law ($ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc} $)
- Ampere's Law provides a powerful way to calculate magnetic fields for highly symmetric current distributions.
- It relates the line integral of the magnetic field around a closed loop to the total current enclosed by that loop.
- Use the Right-Hand Rule: Point your thumb in the direction of the current, and your curled fingers indicate the direction of the magnetic field lines.
Controls
Interactive Hint
Drag the orange "Test Point" on the canvas to begin!