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

Electric potential ($V$) is a characteristic of the electric field itself at a particular point in space, defined as the potential energy per unit positive test charge. It tells us how much potential energy a unit charge *would have* if placed there. Electric potential energy ($U$), on the other hand, is the actual energy stored by a *specific charge* $q$ when it is placed at a point where the potential is $V$. The relationship is $U = qV$. Think of potential as the 'height' of an electric hill, and potential energy as the energy a specific 'ball' (charge) has at that height.

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

Electric potential is defined based on the work done, which is a scalar quantity. Work involves the dot product of force and displacement, resulting in a scalar value. Since potential is work done per unit charge, it also remains a scalar. Electric field, however, is defined as the force per unit charge, and force is a vector quantity (having both magnitude and direction). Therefore, the electric field inherits the vector nature of force, indicating the direction in which a positive test charge would experience a force.

Why do we take infinity as the reference point for zero potential?

Choosing infinity as the reference point for zero potential is a convention that simplifies calculations, especially for isolated charge distributions that extend over finite regions. At infinite distance, the electric force due to a finite charge distribution becomes negligible, making the work done to bring a charge from infinity a convenient and well-defined measure of potential. While other reference points can be chosen, infinity provides a universal and consistent baseline.

How does the electric potential vary with distance from a point charge?

For a point charge $Q$, the electric potential $V$ varies inversely with the distance $r$ from the charge, i.e., $V propto 1/r$. This means as you move further away from the charge, the magnitude of the potential decreases. In contrast, the electric field $E$ varies inversely with the square of the distance, $E propto 1/r^2$. So, potential falls off less rapidly than the electric field with increasing distance.

What is an equipotential surface for a point charge?

An equipotential surface is a surface over which the electric potential is constant. For a single isolated point charge, the equipotential surfaces are concentric spheres centered on the charge. This is because the potential $V = kQ/r$ depends only on the distance $r$. Any point at the same distance $r$ from the point charge will have the same potential. Moving a test charge along an equipotential surface requires no work, as there is no change in potential energy.

Can electric potential be negative? What does it signify?

Yes, electric potential can be negative. If the source charge $Q$ is negative, then the potential $V = kQ/r$ will be negative. A negative potential signifies that positive work would be done *by* the electric field (or negative work by an external agent) to bring a positive test charge from infinity to that point. In essence, the field 'pulls' the positive test charge in, meaning it naturally moves towards the negative source charge, losing potential energy in the process.

Potential due to Point Charge

Physics

NEET UG

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), also known as Volts (V). For a single isolated point charge $Q$ , the electric potential $V$ at a distance $r$ from the charge is gi…

Quick Summary

Electric potential due to a point charge is a fundamental concept in electrostatics, defining the 'electric state' of a point in space. It is a scalar quantity, measured in Volts (V), and represents the work done per unit positive test charge to bring it from infinity to that point without acceleration.

For an isolated point charge $Q$ , the potential $V$ at a distance $r$ is given by $V = \frac{kQ}{r}$ , where $k = \frac{1}{4piepsilon_0}$ . The sign of $Q$ is crucial: positive charges create positive potentials, and negative charges create negative potentials.

Unlike the electric field, which is a vector and varies as $1/r^2$ , potential is a scalar and varies as $1/r$ . This scalar nature simplifies calculations for multiple charges, as the total potential at a point is simply the algebraic sum of potentials due to individual charges (superposition principle).

Understanding this concept is vital for comprehending electric potential energy, work done in electric fields, and the behavior of charges in various electrostatic setups.

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Key Concepts

Derivation from Work Done

The potential at a point is derived by calculating the work done by an external agent to move a unit positive…

Superposition Principle for Potential

Since potential is a scalar, the total potential at any point due to a system of point charges is the…

Potential Difference and Work Done

The potential difference $Delta V = V_B - V_A$ between two points A and B is the work done per unit positive…

Definition: — Work done by external agent to bring unit positive charge from infinity to a point.

Formula: —

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

Units: — Volt (V) or J/C

Nature: — Scalar quantity (includes sign of Q)

Sign: — Positive for +Q, Negative for -Q

Dependence: —

V \propto 1/r

Superposition: —

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

(algebraic sum)

Work Done: —

W_{ext} = q(V_{final} - V_{initial})

Relationship with E: —

E = -dV/dr

(in 1D),

r = V/E

(for point charge)

Equipotential Surfaces: — Concentric spheres for point charge;

W=0

along them.

To remember the potential formula and its properties:

Very Positive Charges Radiate Potential, Negative Charges Attract Negative Potential.

Very: Voltage (Potential)

Positive Charges:

Q

is positive

Radiate Potential:

V

is positive

Negative Charges:

Q

is negative

Attract Negative Potential:

V

is negative

And for the formula: Very Kool Quick Review: $V = kQ/r$