What is the difference between electric potential and electric potential energy?

Electric potential ($V$) is a property of the electric field itself at a given point in space, defined as the potential energy per unit positive test charge ($V = U/q_0$). It tells us how much potential energy a unit charge would have if placed at that point. Electric potential energy ($U$), on the other hand, is the actual energy stored in a specific charge ($q$) when it is placed at a point with potential $V$, given by $U = qV$. So, potential is a characteristic of the location, while potential energy is a characteristic of a specific charge at that location.

Why is electric potential a scalar quantity while electric field is a vector quantity?

Electric potential is defined based on the work done to move a charge, and work is a scalar quantity (it only has magnitude, not direction). Therefore, electric potential, being work done per unit charge, is also a scalar. In contrast, the electric field is defined as the force experienced by a unit positive test charge, and force is a vector quantity (having both magnitude and direction). Hence, the electric field is a vector. This scalar nature of potential often simplifies calculations significantly.

Can electric potential be negative? What does a negative potential signify?

Yes, electric potential can be negative. A negative potential at a point means that an external agent would have to do negative work (or the electric field would do positive work) to bring a unit positive test charge from infinity to that point. This typically occurs in the vicinity of negative source charges. For instance, near a single negative point charge, the potential is negative. It implies that a positive test charge would be attracted to the source charge, and thus, its potential energy would decrease as it approaches.

Is it possible for the electric field to be zero at a point where the electric potential is non-zero, or vice-versa?

Yes, both scenarios are possible. Consider the interior of a charged conducting sphere: the electric field is zero everywhere inside, but the electric potential is constant and equal to the potential on its surface (which is non-zero). Conversely, consider the equatorial plane of an electric dipole: the electric potential is zero at all points on this plane, but the electric field is definitely non-zero and points perpendicular to the dipole axis. This highlights that E and V are related but not directly proportional in a simple way.

How is electric potential related to the electric field?

The electric field (a vector) is related to the electric potential (a scalar) through a mathematical operation called the negative gradient. Specifically, $\vec{E} = -\nabla V$. In simpler terms, the electric field points in the direction of the steepest decrease in electric potential. The magnitude of the electric field is the rate of change of potential with respect to distance. This relationship is crucial because it allows us to derive the electric field from the potential, which is often easier to calculate due to its scalar nature.

Electric Potential

Q: What are equipotential surfaces? Give an example.

Equipotential surfaces are imaginary surfaces in an electric field where all points on the surface have the same electric potential. No work is done by the electric field when a charge moves from one point to another on the same equipotential surface. A key property is that electric field lines are always perpendicular to equipotential surfaces. For example, for an isolated positive point charge, the equipotential surfaces are concentric spheres centered on the charge. For a uniform electric field, the equipotential surfaces are planes perpendicular to the direction of the field lines.

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Version 1Updated 22 Mar 2026

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Electric potential at a point in an electric field is defined as the amount of work done by an external agent in bringing a unit positive test charge from infinity to that point without acceleration. It is a scalar quantity and is measured in Joules per Coulomb (J/C), which is also known as Volt (V). The concept of electric potential is fundamental to understanding the energy associated with elect…

Quick Summary

Electric potential ( $V$ ) is a scalar quantity representing the work done per unit positive test charge to bring it from infinity to a specific point in an electric field, without acceleration. Its unit is the Volt (V), where $1\,\text{V} = 1\,\text{J/C}$ .

The potential due to a point charge $Q$ at a distance $r$ is $V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$ . For a system of charges, the total potential is the algebraic sum of individual potentials. Electric potential difference ( $\Delta V$ ) between two points A and B is the work done by an external agent per unit charge to move it from A to B.

Equipotential surfaces are regions where the potential is constant, and electric field lines are always perpendicular to them. The electric field $\vec{E}$ is the negative gradient of the potential, $\vec{E} = -\nabla V$ .

Electric potential energy ( $U$ ) of a charge $q$ at a potential $V$ is $U = qV$ . For a system of two charges $q_1, q_2$ separated by $r$ , $U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}$ . A dipole $\vec{p}$ in an external field $\vec{E}$ has potential energy $U = -\vec{p} \cdot \vec{E}$ .

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Electric Potential (V): — Work done per unit charge from infinity to a point. Scalar quantity. Unit: Volt (V) or J/C.

Potential due to Point Charge: —

V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r} = \frac{kQ}{r}

Potential due to System of Charges: —

V_{total} = \sum V_i = \sum \frac{kQ_i}{r_i}

(algebraic sum).

Potential Difference: —

\Delta V = V_B - V_A = \frac{W_{ext}}{q_0}

Work Done: —

W = q(V_B - V_A)

Electric Potential Energy (U): — Energy of a charge

q

at potential

V

U = qV

. Unit: Joule (J).

Potential Energy of Two Charges: —

U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r_{12}} = \frac{kq_1q_2}{r_{12}}

Potential Energy of Dipole in E-field: —

U = -\vec{p} \cdot \vec{E} = -pE \cos\theta

Relation between E and V: —

\vec{E} = -\nabla V

(or

E_x = -\frac{dV}{dx}

in 1D).

Equipotential Surfaces: — Surfaces of constant potential. Electric field lines are perpendicular to them. No work done along them.

To remember the relationship between Electric Field and Potential: Electric field Decreases Voltage. Think of 'EDV' as 'Electric Drives Voltage'. The negative sign implies the field points in the direction of decreasing potential.