Biot-Savart Law
Draw wire, see B-field. Builds on Lorentz Force.
A long straight wire carries a steady current flowing upward (toward the top of the screen). You stand to the right of the wire, looking at it. A compass is placed at your position.
In which direction does the compass needle point?
The compass points out of the screen! The magnetic field around a current-carrying wire doesn’t point toward or away from it — it wraps around the wire in concentric circles. Using the right-hand rule (thumb = current direction, fingers = field direction), the field to the right of an upward current points out of the screen.
Loading simulation…
Watch the circular field lines wrap around the wire. Move your cursor to see the field direction at any point. Try increasing the current to see the field get stronger. Notice how it weakens with distance.
B = μ₀I / (2πr)
The field wraps in circles around the wire, falls off as 1/r, and its strength is proportional to the current. This is the foundation for understanding all magnetic fields created by currents.
Every electromagnet works because current creates a magnetic field. Wrapping wire into coils concentrates the field, and adding an iron core amplifies it. From MRI machines to junkyard cranes, it all starts with Biot-Savart.
Your phone’s wireless charger uses a coil of wire carrying alternating current. The magnetic field from this coil induces current in a matching coil inside your phone — all governed by the Biot-Savart law.
High-voltage power lines create magnetic fields that extend into nearby buildings. The Biot-Savart law predicts how these fields decrease with distance, informing safety guidelines for homes near power lines.
The Earth’s magnetic field is generated by enormous currents in the molten iron outer core. These convection currents create magnetic fields via Biot-Savart, forming the geodynamo that shields us from solar radiation.
“Every current makes a magnetic field that wraps around it in circles. One law — Biot-Savart — predicts the field from any shape of wire, from a straight line to a solenoid to the swirling currents inside the Earth.”
Wire Field Lab
Explore the magnetic field created by different wire configurations. Start with a straight wire, then switch to a current loop or solenoid. Move a probe anywhere to measure the field strength and direction. See how the field changes with current and distance.
Loading simulation…
Start with a straight wire and move the probe around it. Watch the field vectors form circles. Now increase the current — all the arrows get longer. Switch to the current loop preset and notice how the field inside the loop is stronger and more uniform. Finally, try the solenoid preset and see the nearly uniform field inside. Move the probe outside the solenoid — the field is almost zero!
A straight wire creates circular field lines that weaken as 1/r. A loop concentrates the field at its center. A solenoid (many loops) creates a nearly uniform field inside and almost zero field outside — it’s like a magnetic bottle. All of these follow from the Biot-Savart law.