Ampère's Law & Solenoids
Wrap coils, see field. Builds on Biot-Savart Law.
You have a very long solenoid — a tightly wound coil of wire carrying a steady current. You can measure the magnetic field at different locations: inside the solenoid (near the center), inside but near the walls, and outside the solenoid.
Where is the magnetic field strongest?
The field is uniform everywhere inside the solenoid! This is one of the most beautiful results in physics. Ampère’s law shows that inside an ideal (infinitely long) solenoid, B = μ₀nI everywhere — independent of position. And outside? The field is zero. The solenoid is a perfect magnetic container.
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Look at the field arrows inside the solenoid — they’re all the same length and direction. Move the probe around inside: the field is constant. Now move outside: it drops to nearly zero.
B = μ₀nI
More turns per meter or more current = stronger field. The field doesn’t depend on position inside — it’s uniform. And outside: zero. The solenoid is a perfect magnetic bottle.
An MRI scanner is essentially a giant superconducting solenoid creating a uniform 1.5–3 T field. The uniformity is critical — any field variation would distort the medical image. B = μ₀nI at industrial scale.
Your car’s fuel injectors, washing machine water valves, and HVAC systems all use solenoid valves. Current through a coil creates a magnetic field that pulls a plunger, opening or closing the valve.
The Large Hadron Collider uses thousands of superconducting solenoids to focus and steer particle beams. The uniform field inside each solenoid keeps the beam tightly collimated over kilometers.
Every speaker has a permanent magnet shaped like a solenoid’s field. A voice coil carrying audio-signal current sits in this field, and the Lorentz force pushes it back and forth, creating sound waves.
“Wrap a wire into a coil, run current through it, and you get a perfectly uniform magnetic field inside and zero outside. Ampère’s law makes the solenoid one of the most useful devices in all of physics and engineering.”
Solenoid Lab
Build your own solenoid and explore the magnetic field everywhere. Adjust the number of turns, current, and length. Insert a field probe anywhere to measure the field strength. Compare the solenoid with a single current loop to see how stacking loops creates uniformity.
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Start with 10 turns and watch the field arrows inside — they’re nearly uniform. Increase to 30 turns: the field gets three times stronger and even more uniform. Now double the current — the field doubles too (B = μ₀nI). Move the probe outside the solenoid: the field is nearly zero. Switch to the single loop preset and compare — the field inside a single loop is far from uniform.
A solenoid creates a uniform magnetic field B = μ₀nI inside and essentially zero field outside. More turns per length or more current = stronger field. This uniformity makes solenoids indispensable in MRI machines, particle accelerators, and countless electromagnetic devices.