Electric Potential
Electric potential at a point in space is the amount of electric potential energy per unit positive test charge at that location, representing the work done per unit charge to bring a positive test charge from infinity to that point against the electric field. It is a scalar quantity measured in volts (V), where 1 volt equals 1 joule per coulomb. Electric potential is fundamental to understanding capacitors, batteries, and electrical circuits, and the difference in electric potential between two points (voltage) drives the flow of electric current.
Key Formula
V = W / q = k × Q / r
LaTeX: V = \frac{W}{q} = \frac{kQ}{r}
| Symbol | Meaning | Unit |
|---|---|---|
| V | Electric potential | V (volts) |
| W | Work done in bringing test charge from infinity | J |
| q | Test charge | C |
| k | Coulomb's constant (8.988 × 10⁹) | N·m²/C² |
| Q | Source charge creating the potential | C |
| r | Distance from source charge | m |
Worked Example
Problem
A point charge Q = +8 μC is located in vacuum. Calculate the electric potential at a distance of 0.5 m from the charge, and the work done to bring a +3 μC charge from infinity to this point.
Solution
Step 1: Calculate electric potential at r = 0.5 m. V = k × Q / r V = (8.988 × 10⁹) × (8 × 10⁻⁶) / 0.5 V = (71904) / 0.5 = 143,808 V ≈ 1.44 × 10⁵ V Step 2: Work done to bring q = 3 × 10⁻⁶ C from infinity to this point. W = q × V = 3 × 10⁻⁶ × 1.44 × 10⁵ = 0.432 J
Answer
V ≈ 1.44 × 10⁵ V; W ≈ 0.43 J
Electric Potential vs. Electric Field — Key Differences
| Property | Electric Potential (V) | Electric Field (E) | Relationship |
|---|---|---|---|
| Nature | Scalar quantity | Vector quantity | E = −dV/dr |
| SI Unit | Volt (V = J/C) | N/C or V/m | 1 V/m = 1 N/C |
| Formula (point charge) | V = kQ/r | E = kQ/r² | V has 1/r dependence |
| At infinity | V → 0 | E → 0 | Both vanish at infinity |
| Superposition | Algebraic sum of scalars | Vector sum | Potentials add as numbers |
Interactive Tools
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Related Terms
Electric Field
An electric field is a vector field that exists in the region around an electric charge or a changing magnetic field, representing the electrostatic force that would be exerted per unit positive charge placed at any point in space. The field lines emanate outward from positive charges and point inward toward negative charges, with the density of field lines indicating field strength. Electric fields are central to understanding capacitors, electromagnetic waves, semiconductor devices, and the operation of all electrical equipment from simple circuits to complex communication systems.
Voltage (Potential Difference)
Voltage, or potential difference, is the difference in electric potential between two points in a circuit or electric field, representing the work done per unit positive charge to move it from one point to another against or with the electric force. Measured in volts (V), it is the driving force (electromotive force) that causes electric current to flow through a conductor from higher to lower potential. Voltage is the key parameter in electrical engineering and electronics, governing the operation of batteries, power supplies, electronic components, and all forms of electrical power transmission.
Electric Charge
Electric charge is a fundamental intrinsic property of matter that causes particles to experience a force when placed in an electromagnetic field, existing as either positive (carried by protons) or negative (carried by electrons) with an elementary charge unit of e = 1.602 × 10⁻¹⁹ coulombs. Charge is conserved in all physical processes (the total charge of an isolated system remains constant), and it is quantised, meaning any observable charge is an integer multiple of the elementary charge. Electric charge is the source of the electric force, which is described by Coulomb's Law and governs all electromagnetic interactions in nature and technology.
From Latin "potentia" (power, capability) and "electricus" (produced from amber). The concept was developed by Carl Friedrich Gauss and George Green in the 1820s–1830s. The unit volt is named after Alessandro Volta (1745–1827), inventor of the voltaic pile (first battery).