Electric Potential Energy and Potential Difference Study Pack
Kibin's free study pack on Electric Potential Energy and Potential Difference includes a 6-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 28, 2026
Electric Potential Energy and Potential Difference Study Guide
Unpack the relationship between electric potential energy, voltage, and charge movement — covering ΔV = W/q, equipotential surfaces, the electron volt, and how field strength links to potential difference via ΔV = −Ed.
Key Takeaways
- •Electric potential energy is the work done by an external force to move a charge against an electric field, stored as energy in the charge-field system.
- •Electric potential (voltage) is the potential energy per unit charge at a point in a field, measured in volts (1 V = 1 J/C), and is independent of the test charge used to measure it.
- •The potential difference between two points equals the work done per unit charge to move a positive test charge from one point to the other: ΔV = W/q.
- •Positive charges naturally move from regions of high potential to low potential, while negative charges move from low to high potential — both moving toward lower potential energy.
- •The electron volt (eV) is a convenient unit of energy for atomic-scale systems, defined as the kinetic energy gained by one elementary charge accelerated through a potential difference of 1 volt (1 eV = 1.6 × 10⁻¹⁹ J).
- •In a uniform electric field, potential difference and field strength relate by ΔV = −Ed, where d is the displacement parallel to the field direction.
- •Equipotential surfaces are perpendicular to electric field lines at every point, and no work is done moving a charge along an equipotential surface.
Electric Potential Energy in a Field
Just as a mass held above the ground stores gravitational potential energy, a charged particle in an electric field stores electric potential energy that depends on its position relative to the source of that field.
Origin of Electric Potential Energy
- •Electric potential energy arises from the interaction between a charged particle and the electric field produced by other charges.
- •When an external force moves a positive charge from point A to point B against the direction of the electric force, that external agent does positive work, and this work is stored as increased potential energy in the system.
- •Conversely, if the electric force itself does positive work on the charge (moving it in the direction of the field), the system loses potential energy and the charge gains kinetic energy.
Work-Energy Relationship for Charges
- •The work W done by the electric force on a charge q moving between two points is related to the change in electric potential energy by: W = −ΔPE, or equivalently ΔPE = −W.
- •This sign convention means that when the electric field does positive work, potential energy decreases — parallel to how gravity does positive work on a falling object while gravitational potential energy decreases.
- •For a positive charge in a uniform electric field pointing from a positive plate to a negative plate, moving the charge in the direction of the field decreases its electric potential energy.
Electric Potential and Voltage
Electric potential is a scalar quantity assigned to every point in an electric field that describes how much potential energy a unit positive charge would have if placed at that point.
Defining Electric Potential
- •Electric potential V at a point is defined as the electric potential energy PE of a small positive test charge q placed at that point, divided by the magnitude of that charge: V = PE/q.
- •The unit of electric potential is the volt (V), where 1 volt equals 1 joule per coulomb (1 V = 1 J/C).
- •Because potential is potential energy divided by charge, it is a property of the field at a location — not of any particular charge placed there.
Potential Difference (Voltage)
- •The potential difference ΔV between two points A and B is defined as ΔV = V_B − V_A = W/q, where W is the work done by an external agent moving charge q from A to B.
- •Potential difference is commonly called voltage and is the physically meaningful quantity measured in circuits and experiments — absolute potential requires an arbitrary reference point (often set to zero at infinity or at ground).
- •A positive potential difference from A to B means point B is at a higher potential; a positive charge released between these points would spontaneously move from B toward A (high to low potential).
Direction of Spontaneous Charge Motion
- •Positive charges accelerate from regions of higher potential toward regions of lower potential, analogous to how masses fall from higher to lower gravitational potential.
- •Negative charges behave oppositely — they accelerate from lower potential toward higher potential — because their potential energy is negative times the field's potential.
- •In both cases, the charge moves to minimize the system's potential energy, gaining kinetic energy in the process.
Uniform Electric Fields and the Relationship Between Potential and Field Strength
In a uniform electric field — such as the field between two large parallel charged plates — the relationship between electric field strength and potential difference takes a clean, linear form that is especially useful for calculations.
Potential Difference Across a Uniform Field
- •For a uniform electric field E directed from a positive plate to a negative plate, the potential difference between the plates separated by distance d is given by ΔV = Ed, or equivalently E = ΔV/d.
- •This means the electric field strength (in N/C) is numerically equal to the potential gradient (in V/m) — the two units are equivalent: 1 N/C = 1 V/m.
- •The positive plate is always at the higher potential and the negative plate at the lower potential, so the field vector always points in the direction of decreasing potential.
Sign Convention with Displacement
- •More precisely, the relationship is ΔV = −Ed, where d is the displacement measured in the same direction as the electric field E.
- •Moving a positive test charge in the direction of the field (toward the negative plate) decreases the potential (ΔV is negative), consistent with the formula.
- •Moving the charge against the field (toward the positive plate) increases the potential (ΔV is positive), requiring external work input.
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Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.
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What is the SI unit of electric potential, and how is it defined?
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Electric Potential Energy
Explain electric potential energy in your own words. How does it arise, and how does it change when a charge moves with or against an electric field?
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