Electric Potential

Contents

Key Stage 5

Meaning

Electric potential at a point in an electric field is the work done per unit charge to move a small positive test charge from infinity to that point.

About Electric Potential

• Electric potential is denoted by the symbol 𝑉.
• Electric potential is measured in volts (V).
• The electric potential difference (pd) between two points is the work done to move a unit charge between those points.
• Equipotential surfaces are surfaces on which the electric potential is the same; no work is required to move a charge along an equipotential surface.

Formula

Electric potential is given by the general formula:

• \(𝑉=\frac{𝑊}{𝑄}\)

Where:

• 𝑉 is the electric potential
• 𝑊 is the work done
• 𝑄 is the charge

The electric potential due to a point charge is

• \(𝑉=𝑘\frac{𝑄}{𝑟}\)

Where:

• 𝑘 is the Coulomb's constant
• 𝑄 is the point charge causing the field
• 𝑟 is the distance from that point charge

Since;

• \(𝑘=\frac{1}{4\pi\varepsilon_0}\)

Then:

• \(𝐸=\frac{1}{4\pi\varepsilon_0}\frac{𝑄}{𝑟}\)

or

• \(𝐸=\frac{𝑄}{4\pi\varepsilon_0𝑟}\)

Where:

• \(\varepsilon_0\)is the permittivity of free space