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

Electric potential ($V$) is a scalar quantity defined at a point in an electric field, representing the work done per unit positive test charge to bring it from infinity to that point. Its unit is Volts (J/C). Electric potential energy ($U$), on the other hand, is the energy possessed by a specific charge or system of charges due to its position in an electric field. It's the total work done to bring that particular charge from infinity to its current position. Its unit is Joules (J). The relationship is $U = qV$, where $q$ is the charge.

Why do we consider an 'external' field when discussing potential energy?

We consider an 'external' field to simplify the problem. When we talk about the potential energy of a charge $q$ in an external field, we are focusing on the interaction of $q$ with a pre-existing field created by other charges. This means we don't have to consider the field created by $q$ itself, which would make the calculation more complex. If we were to calculate the potential energy of a system of charges, we would include both the potential energy of each charge in the external field and the interaction potential energy between the charges within the system.

What does a negative potential energy signify?

A negative potential energy generally indicates an attractive interaction or a more stable configuration. For example, if a positive charge is placed in a region of negative potential, its potential energy ($U=qV$) will be negative, indicating that work was done by the electric field to bring it there, or that it is in a bound state. For a dipole, $U = -vec{p} cdot vec{E}$, so when the dipole moment is aligned with the electric field ($ heta=0^circ$), $U = -pE$, which is the minimum potential energy and represents a stable equilibrium.

How is the work done by an external agent related to the change in potential energy?

If an external agent moves a charge from one point to another without accelerating it (i.e., its kinetic energy remains constant), then the work done by the external agent ($W_{ext}$) is exactly equal to the change in the system's potential energy ($Delta U$). That is, $W_{ext} = U_f - U_i = Delta U$. This is because the external agent must do work against the conservative electrostatic force, and this work is stored as potential energy.

What is the potential energy of an electric dipole in a uniform electric field, and when is it maximum or minimum?

The potential energy of an electric dipole with dipole moment $vec{p}$ in a uniform external electric field $vec{E}$ is given by $U = -vec{p} cdot vec{E} = -pE cos heta$, where $ heta$ is the angle between $vec{p}$ and $vec{E}$. The potential energy is minimum (most stable equilibrium) when $ heta = 0^circ$ (dipole aligned with the field), giving $U = -pE$. It is maximum (unstable equilibrium) when $ heta = 180^circ$ (dipole anti-aligned with the field), giving $U = +pE$.

Does the potential energy of a system of charges depend on the path taken to assemble them?

No, the potential energy of a system of charges, or a charge in an external field, does not depend on the path taken to assemble the configuration. This is because the electrostatic force is a conservative force. The work done by a conservative force, and thus the change in potential energy, depends only on the initial and final positions, not on the trajectory between them. This property allows us to define a unique potential energy for any given configuration.

Potential Energy in External Field

Physics

NEET UG

Version 1Updated 22 Mar 2026

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Potential energy in an external electric field refers to the energy possessed by a charge or a system of charges, or an electric dipole, due to its position within an electric field generated by sources external to the charge(s) or dipole itself. This energy is a scalar quantity and represents the work done by an external agent in bringing the charge(s) or dipole from infinity (or a reference poin…

Quick Summary

Potential energy in an external electric field is the energy a charge or a system of charges possesses due to its position within a pre-existing electric field. For a single point charge $q$ at a location where the external potential is $V$ , its potential energy is $U = qV$ .

This represents the work an external agent must do to bring the charge from infinity to that point without acceleration. For a system of two charges $q_1$ and $q_2$ at $vec{r_1}$ and $vec{r_2}$ respectively, the total potential energy includes their individual potential energies in the external field and their mutual interaction energy: $U = q_1 V(vec{r_1}) + q_2 V(vec{r_2}) + \frac{1}{4piepsilon_0} \frac{q_1 q_2}{r_{12}}$ .

For an electric dipole with moment $vec{p}$ in a uniform external electric field $vec{E}$ , its potential energy is $U = -vec{p} cdot vec{E}$ . This energy is minimum when the dipole aligns with the field ( $heta=0^circ$ ) and maximum when it is anti-aligned ( $heta=180^circ$ ).

Understanding these formulas and their sign conventions is crucial for NEET, as they govern the behavior of charges and dipoles in electric environments.

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Key Concepts

Potential Energy of a Single Charge in an External Potential

The potential energy $U$ of a point charge $q$ placed at a point where the electric potential due to an…

Potential Energy of a System of Two Charges in an External Field

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Potential Energy of an Electric Dipole in a Uniform External Electric Field

An electric dipole, characterized by its dipole moment $vec{p}$ , experiences a torque in an external electric…

Single Charge: —

U = qV

System of Two Charges: —

U = q_1 V_1 + q_2 V_2 + k \frac{q_1 q_2}{r_{12}}

Electric Dipole (Uniform Field): —

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

Work Done by External Agent (no $Delta K$): —

W_{ext} = Delta U = U_f - U_i

Work Done by Electric Field: —

W_{field} = -Delta U = U_i - U_f

Stable Equilibrium (Dipole): —

heta = 0^circ

U_{min} = -pE

Unstable Equilibrium (Dipole): —

heta = 180^circ

U_{max} = +pE

Reference Point: —

U=0

at infinity (for charges),

U=0

heta=90^circ

(for dipoles).

PE = qV, Dipole = -pE cos(theta) -> 'PE is qV, Dipole's PE is Negative PE Cost (of theta)'