Electrostatic Potential
Topographic voltage map. Builds on Electric Field Lines.
Two points in space are at different electric potentials: point A is at +100 V and point B is at +50 V. You place a small positive test charge at point A and release it from rest. There are no other forces acting on the charge.
Where does the charge go?
The positive charge moves from A to B — from high potential to low potential! Electric potential is like an altitude map for charges. Positive charges ‘fall’ from high voltage to low voltage, just as a ball rolls from a hilltop down to a valley. The electric field always points from high to low potential, and positive charges follow the field.
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Drag the positive test charge around the landscape and watch it accelerate downhill — from high voltage (red peaks) to low voltage (blue valleys). Toggle the electric field arrows to see how they always point downhill.
V = kq / r
Potential is energy per charge. Positive charges roll ‘downhill’ from high V to low V. Negative charges roll ‘uphill.’ The potential difference between two points is what we call voltage.
A 9V battery maintains a 9-volt potential difference between its terminals. Electrons flow from the negative terminal (low potential for them) through the circuit to the positive terminal, powering everything along the way.
A defibrillator charges capacitors to thousands of volts, then discharges across the chest. The huge potential difference drives current through the heart muscle, resetting its rhythm.
Your neurons maintain a -70 mV resting potential across their membranes. When a nerve fires, ion channels open and the voltage spikes to +40 mV — that voltage pulse IS the signal racing through your body.
Power plants transmit electricity at hundreds of thousands of volts. Higher voltage means less current for the same power, which means less energy lost to resistance in the wires.
“Voltage is the altitude map of the electric world. Charges roll downhill, currents flow from high to low, and every battery, nerve, and lightning bolt is just nature following the gradient.”
Voltage Landscape
Build your own electric potential landscape by placing positive and negative charges. Watch the voltage map form as a 3D terrain — peaks around positive charges, valleys around negative ones. Then release test charges and watch them roll downhill through your custom potential landscape.
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Start with a single positive charge and watch the voltage peak form around it. Release a positive test charge nearby — it rolls downhill, away from the source. Now add a negative charge nearby to create a dipole: one peak, one valley, with a saddle point between them. Release a test charge in the saddle region and watch it navigate the terrain. Try surrounding a region with charges to create a ‘voltage bowl’ that traps test charges inside.
Electric potential is a scalar field — just a number at every point. But from that single number, you can reconstruct everything: the electric field is the slope, the force is the slope times the charge, and the motion follows the terrain. One scalar encodes the whole story.