Magnetic Field Energy
Energy in inductor’s field. Builds on Inductance & RL Circuits.
A large superconducting coil (inductor) is carrying a steady current of 1000 amps. The magnetic field inside is enormous. You suddenly cut off the power supply while keeping the circuit closed through a resistor.
Where was the energy stored while the current was flowing?
The energy lives in the magnetic field! An inductor stores energy U = ½L I², and this energy physically resides in the magnetic field filling the coil’s interior. The energy density at any point is u = B²/(2μ₀). When the current decays through the resistor, the magnetic field collapses and all that stored energy is converted to heat.
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Watch the magnetic field grow as the inductor charges up. The energy bar shows U = ½LI² filling in real time. When you discharge, the field collapses and energy transfers to the resistor.
U = ½LI² = B²V/(2μ₀)
Double the current, quadruple the stored energy. The energy is physically in the magnetic field — fields are real, and they carry energy.
A hospital MRI stores about 5 megajoules of energy in its superconducting magnet — equivalent to the kinetic energy of a car traveling at 250 km/h. A “quench” (sudden loss of superconductivity) releases all this energy as heat, boiling hundreds of liters of liquid helium.
Power companies store grid energy in enormous superconducting coils. Because there’s no resistance, the current flows indefinitely and the energy stored in the magnetic field can be retrieved at nearly 100% efficiency.
Railguns store megajoules of energy in inductor banks. When discharged in milliseconds, the energy in the collapsing magnetic field accelerates a projectile to hypersonic speeds.
Every phone charger and laptop adapter uses inductors to temporarily store energy in their magnetic fields during the voltage conversion process, cycling millions of times per second.
“Fields are not mathematical fictions. The magnetic field inside an MRI machine holds enough energy to launch a car at highway speed. That energy is real, it’s in the field, and it can do real work.”
Magnetic Energy Lab
Explore energy storage in inductors and LC circuits. Watch energy flow between the magnetic field (inductor) and electric field (capacitor) in real time. Adjust L, C, and initial current to see how the oscillation changes.
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Start in “Inductor Only” mode. Charge the inductor and watch the energy bar fill as the field grows inside the solenoid. Now switch to LC mode: connect a capacitor and watch the energy oscillate between magnetic and electric fields. Try increasing L — the oscillation slows down. Try increasing C — it slows down too. The frequency is f = 1/(2π√(LC)).
An LC circuit is the electromagnetic version of a mass on a spring. The inductor (L) is the mass (stores kinetic energy as magnetic field energy), and the capacitor (C) is the spring (stores potential energy as electric field energy). Energy sloshes back and forth forever — unless resistance dissipates it.