Define Electric Potential- Physics Concepts

What Is Electric Potential?

Electric potential is the amount of work needed to move a unit positive charge from infinity to a specific point in an electric field, without accelerating it. That's the textbook definition. Here's what it actually means:

Think of it like gravitational potential. A ball held high has potential energy because of its position. Similarly, a charge in an electric field has potential energy because of where it sits.

Electric potential (V) is that energy per unit charge. It's measured in Volts (V), which is why people sometimes call it "voltage."

Electric Potential vs Electric Potential Energy

Students mix these up constantly. Don't.

• Electric Potential (V) — energy per unit charge, measured in Volts. It's a property of the point in space.
• Electric Potential Energy (U) — total energy a charge has due to its position. Measured in Joules.

The relationship is simple:

U = qV

Where q is the charge in Coulombs. If you have a 2 Coulomb charge at a point with 5 Volts potential, its potential energy is 10 Joules.

The Formula

For a point charge, electric potential is:

V = kq / r

Where:

• V = electric potential in Volts
• k = Coulomb's constant (8.99 × 10⁹ N⋅m²/C²)
• q = the source charge in Coulombs
• r = distance from the charge in meters

This equation assumes you're working with a point charge. For more complex charge distributions, you'll need to integrate.

Key Properties

Scalar Quantity

Electric potential is a scalar, not a vector. It has magnitude but no direction. This makes calculations easier — you just add potentials algebraically instead of dealing with vector components.

Sign Matters

Potential can be positive or negative depending on the source charge. A positive charge produces positive potential. A negative charge produces negative potential.

Two positive charges far apart might both have positive potential at your point of interest. Add those potentials together. Simple.

Reference Point

Potential is always measured relative to a reference point. Usually infinity, where potential is defined as zero. In circuits, we use ground (0V) as the reference.

Calculating Electric Potential: How To

Example 1: Point Charge

Find the potential 0.5 meters from a 3 μC charge.

Given: q = 3 × 10⁻⁶ C, r = 0.5 m, k = 8.99 × 10⁹ N⋅m²/C²

V = kq / r

V = (8.99 × 10⁹ × 3 × 10⁻⁶) / 0.5

V = 53,940 / 0.5

V = 107,880 Volts (or about 108 kV)

Example 2: Two Point Charges

Find the potential at a point 0.3 m from a +4 μC charge and 0.4 m from a -2 μC charge.

V₁ = (8.99 × 10⁹ × 4 × 10⁻⁶) / 0.3 = 119,867 V

V₂ = (8.99 × 10⁹ × -2 × 10⁻⁶) / 0.4 = -44,950 V

V_total = V₁ + V₂ = 119,867 - 44,950 = 74,917 Volts

Electric Field vs Electric Potential

Here's where people get confused again.

The electric field points in the direction of steepest decrease of potential. That's what the negative sign in E = -dV/dr means.

Equipotential Surfaces

An equipotential surface is a region where potential is constant everywhere. Key facts:

• Electric field lines are always perpendicular to equipotential surfaces
• No work is done moving a charge along an equipotential surface
• Conductors in electrostatic equilibrium are equipotential surfaces

Picture the lines on a topographic map. Each line represents constant elevation (potential energy). You can move along those lines without gaining or losing height. Same idea here.

Common Mistakes to Avoid

• Forgetting the sign — negative charges create negative potential. Don't ignore the sign.
• Confusing units — potential is in Volts, potential energy is in Joules. Different things.
• Using r² in the denominator — that's for electric field. For potential, it's just r.
• Assuming potential is zero between charges — it isn't unless the potentials exactly cancel.

Real-World Applications

Electric potential explains how:

• Batteries work — they maintain a potential difference (voltage) between terminals
• Lightning happens — massive potential buildup between clouds and ground discharges as current
• Capacitors store energy — they hold charge at a specific potential
• Van de Graaff generators — they build up extremely high potentials on a metal dome

Quick Reference Summary

• Electric potential = work per unit charge (Volts)
• Point charge formula: V = kq/r
• It's a scalar — add algebraically
• Related to field by: E = -dV/dr
• Potential energy: U = qV

That's the core of electric potential. Learn the formula, understand the scalar nature, and practice switching between potential, field, and energy. The rest follows from those basics.