Electric Potential and Potential Energy
Potential of point charges and dipoles, equipotential surfaces and energy of a configuration. (Physics › Electrostatics, NEET UG syllabus.)
What is Electric Potential and Potential Energy?
The work done per unit positive test charge by an external agent in bringing it from ∞ to a point in an electric field without acceleration.
Key formula / rule: Electric Potential due to a point charge
Key points
- Define electric potential and electric potential energy.
- Calculate electric potential due to a point charge and a system of point charges.
- Calculate electric potential energy for a system of charges.
- Describe and identify equipotential surfaces.
Common exam trap
Confusing electric potential (scalar) with electric field (vector).
Definitions
- Term
Electric Potential (V)
- Meaning
The work done per unit positive test charge by an external agent in bringing it from ∞ to a point in an electric field without acceleration.
- Term
Electric Potential Energy (U)
- Meaning
The work done by an external agent in assembling a system of charges from ∞ to their current configuration.
- Term
Equipotential Surface
- Meaning
A surface in an electric field where all points on the surface have the same electric potential.
- Term
Electron Volt (eV)
- Meaning
The energy gained by an electron when it is accelerated through an electric potential difference of one volt. (1 eV = 1.602 × 10⁻¹⁹ J).
Learning objectives
Define electric potential and electric potential energy.
Calculate electric potential due to a point charge and a system of point charges.
Calculate electric potential energy for a system of charges.
Describe and identify equipotential surfaces.
Relate electric field and electric potential.
Calculate potential and potential energy for electric dipoles.
Formulae
- Name
Electric Potential due to a point charge
- Note
Q is the charge, r is the distance from the charge. k = 1 / 4πε₀ ≈ 9 x 10⁹ Nm²/C².
- Expression
V = (1 / 4πε₀) * (Q / r)
- Name
Electric Potential due to a system of point charges
- Note
Algebraic sum, considering signs of charges.
- Expression
V = Σᵢ (1 / 4πε₀) * (Qᵢ / rᵢ)
- Name
Electric Potential Energy of two point charges
- Note
r is the separation between q₁ and q₂. Includes signs of charges.
- Expression
U = (1 / 4πε₀) * (q₁q₂ / r)
- Name
Electric Potential Energy of a system of multiple point charges
- Note
Sum over all possible pairs of charges.
- Expression
U = Σ (1 / 4πε₀) * (qᵢqⱼ / rᵢⱼ) for all unique pairs (i, j)
- Name
Relation between Electric Field and Electric Potential
- Note
Electric field points in the direction of decreasing potential.
- Expression
E = -dV/dr (in 1D) or E = -∇V (in 3D)
- Name
Electric Potential due to a short electric dipole (r >> a)
- Note
p is the dipole moment, θ is the angle between the position vector r and p.
- Expression
V = (1 / 4πε₀) * (p cosθ / r²)
- Name
Potential Energy of an electric dipole in a uniform electric field
- Note
p is the dipole moment, E is the electric field strength.
- Expression
U = -p.E = -pE cosθ
Prerequisites
Basic understanding of electric charge and Coulomb's Law.
Concept of electric field and electric field lines.
Work-Energy Theorem and conservative forces.
Vector addition and scalar multiplication.
Common mistakes
Confusing electric potential (scalar) with electric field (vector).
Forgetting to include signs of charges when calculating potential or potential energy.
Incorrectly summing potential energies for multiple charges (summing pairs, not individual charges).
Assuming work is always done when moving a charge in an electric field (work is zero on equipotential surfaces).
Using distance 'r' instead of 'r²' or 'r³' in dipole potential formulas.
Not understanding that potential energy is defined for a system, not a single charge.
Keywords
Electric potential
potential energy
equipotential surfaces
electric dipole
work done
conservative field
volt
electron volt
electrostatic
Practice preview
Calculate the electric potential at a point 9 cm away from a point charge of +3 nC. (Given: k = 9 x 10^9 N m^2 C^-2)…
easy
Two point charges, +2 µC and -4 µC, are placed 10 cm apart in vacuum. What is the electric potential energy of this system? (Given: k = 9 x 10^9 N m^2 C^-2)…
medium
The electric potential at point A is +10 V and at point B is -5 V. What is the work done by the electric field in moving a charge of +2 C from point A to point B?…
medium