Electric Field Energy
Visualize stored energy. Builds on Capacitance.
A capacitor is connected to a power supply and stores exactly 1 joule of energy at 10 V. You then crank the voltage up to 20 V using the same capacitor.
How much energy is now stored in the capacitor?
4 joules! Energy scales as voltage squared: U = ½C V². When you double the voltage from 10 V to 20 V, the energy quadruples from 1 J to 4 J. That innocent-looking ² makes high-voltage capacitors extraordinarily dangerous.
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Adjust the voltage slider and watch the energy bar grow. Notice it curves upward — that’s the V² dependence. Toggle the field view to see where the energy actually lives: spread throughout the electric field between the plates.
U = ½C V² = ½Q V = Q² / 2C
Three formulas, one energy. Use ½CV² when voltage is known, Q²/2C when charge is fixed. The energy lives in the field between the plates, with density u = ½ε₀E².
Military railguns use massive capacitor banks charged to thousands of volts. The V² scaling means enormous energy — enough to launch projectiles at Mach 6.
With capacitances up to thousands of farads, supercapacitors bridge the gap between batteries and regular capacitors, powering buses and regenerative brakes.
Clouds and ground form a giant capacitor. The field energy builds until the air breaks down — a lightning bolt releases billions of joules in milliseconds.
The world’s most powerful lasers are fired by discharging enormous capacitor banks. Petawatts of power for billionths of a second.
“Energy lives in the field, not on the plates. And it goes as V squared — which is why a capacitor at 1000 V stores a million times more energy than one at 1 V.”
Energy Explorer
Visualize where capacitor energy lives. Adjust voltage, capacitance, and plate geometry while watching the energy density field update in real time. Compare the three equivalent energy formulas side by side.
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Start by sweeping the voltage from 0 to max — watch the energy curve. It’s a parabola, not a line! Toggle the field energy density view to see the energy glowing between the plates. Then try changing the plate separation with the battery disconnected: Q stays fixed, but watch what happens to V and U.
U = ½CV² and u = ½ε₀E² are two faces of the same truth: electric fields carry energy. Double the field strength, quadruple the energy density. This V² scaling is why high-voltage systems demand extreme respect.