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Relation of E and V
Intermediate
Field is the negative gradient of potential.
E = −dV/dxThe field is the negative gradient of potential, E = −∇V. In 1D E = −dV/dx; for a uniform field V = Ed.
A 12 V across 2 mm gap: 6000 V/m.
E points toward decreasing V.
In more detail
The electric field is the negative gradient of the potential, E = −dV/dx. The field points from high to low potential, and its strength is the rate of decrease of potential.
Real-world uses
- Calculating fields from measured potential maps.
- Designing electrodes to achieve a target field strength.
- Engineers calculate the field from a measured potential by finding how the potential changes with distance.
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Frequently asked questions
Which way does the field point?
From higher potential towards lower potential.
What units does the field have?
Volts per metre, which equal newtons per coulomb.
Why is there a minus sign?
The field points from high to low potential, so it is the negative of the rate at which the potential increases.
Related topics in Electrostatics
Electric potential · Potential difference · Equipotential surfaces · Electron volt · Potential energy of charges · Capacitor