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Theme D — Fields

D.2.8 Electric Potential Energy — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 23 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

D.2.8 Electric Potential Energy — IB PHYSICS HL notes: Use Ep = kq1q2/r and ΔEp = qΔV for charges, and relate potential energy to force–distance graphs and the electronvolt.System — electric potential energy is stored in a system of charges because of the electric forces between …

  • Definition
  • Single charge
  • Do not square
  • Like charges
  • Energy graph
  • Moving charge

Part 1 of 8Definition

Definition
System
  • System electric potential energy is stored in a system of charges because of the electric forces between them
Definition
  • Definition the work done in bringing all the charges to their positions from infinity
Single charge
  • Ep = qV, where V is the potential at the point
Sign
  • Sign it can be positive or negative, unlike gravitational potential energy

Part 2 of 8Equation for two point charges

Equation
  • Ep = kq1q2/r
Symbols
  • Ep in J, charges in C with signs, r between centres in m and k = 8.99 × 109 N m2 C−2
Zero
  • Ep = 0 at infinity
Do not square
  • Do not square r is not squared in the energy equation

Part 3 of 8Sign of the energy

Like charges
  • Ep is positive because the force is repulsive
  • Work is needed to bring them together and energy is released as they separate
Unlike charges
  • Ep is negative because the force is attractive
  • Energy must be supplied to separate them
Energy graph
  • Energy graph for like charges it falls with distance to zero, for unlike charges it rises to zero
Force
  • Force the gradient of the Ep–r graph gives the force

Part 4 of 8Changes in potential energy

Changes in potential energy
Moving charge
  • ΔEp = kq1q2(1/r1 − 1/r2)
Through a potential difference
  • ΔEp = qΔV
Work by or on the field
  • Work by or on the field work is done on the field to bring like charges together or separate unlike ones, and by the field in the opposite cases
Force–distance graph
  • Force–distance graph the area under it gives the work done, equal to the change in Ep
Analogy
  • Analogy it is like the gravitational case, with a negative charge moving away from a positive charge like a mass lifted

Part 5 of 8Charges accelerated through a potential difference

Energy conservation
  • Energy conservation potential energy lost equals kinetic energy gained
Equation
  • ½mv2 = qV so v = √(2qV/m)
Direction
  • Direction a free positive charge moves towards lower potential and a negative one towards higher potential
Validity
  • Validity ignores relativity, so valid below about 10% of the speed of light
Uses
  • Uses electron guns, particle accelerators and mass spectrometers

Part 6 of 8The electronvolt

Definition
  • Definition the energy gained by an electron or proton accelerated through a potential difference of 1 V
Conversion
  • 1 eV = 1.60 × 10−19 J
Charge
  • Charge a particle of charge 2e gains twice as many eV for the same voltage
Use
  • Use atomic and nuclear energies in eV, keV and MeV

Part 7 of 8Closest approach

Closest approach
Alpha particle and nucleus
  • Alpha particle and nucleus the alpha particle stops momentarily at the closest distance
Energy
  • Energy all the initial kinetic energy is then electric potential energy, kq1q2/r
Total energy
  • Total energy kinetic plus potential energy stays constant under the electric force alone

Part 8 of 8More from the specification

More from the specification
Electric potential in radial fields
  • The electric potential V at distance r from a point charge Q is V = Q / , defined as work done per unit positive charge from infinity.
    • (4 pi epsilon0 r)
Electric potential energy of point charges
  • The mutual electrostatic potential energy of two point charges Q and q is Ep = Q q / .
    • (4 pi epsilon0 r)
Equipotential surfaces and field lines
  • Equipotential surfaces run perpendicular to electric field lines, requiring zero mechanical work to move charges along an equipotential contour.
Uniform field between plates
  • Uniform field between plates electric field strength between parallel charged conducting plates is uniform, with parallel and equidistant field lines.
Equipotential surfaces
  • Equipotential surfaces planes or spheres of constant electric potential are always oriented perpendicularly to local electric field lines.
Coulomb electrostatic potential energy
  • Coulomb electrostatic potential energy electric potential energy between point charges separated by distance r obeys Ep = k q1 q2 / r.
Equipotential
  • A surface of constant potential
Coulomb
  • Charge passing a point when a current of 1 A flows for 1 s.
Parallel
  • Components on separate branches, each with the full e.m.f.
Permittivity
  • A property of a medium affecting the electric force within it.
Current
  • Flow of electrons in a circuit.
Uniform
  • Same density throughout, so the weight acts at the centre.
Density
  • Mass per unit volume.
Field lines
  • Lines showing the direction and strength of a magnetic field.
W = mg
What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg−1 on Earth)

Key terms

TermMeaning
Electric potential energyThe work done in bringing all the charges of a system to their positions from infinity.
Ep = kq1q2/rThe electric potential energy of two point charges.
ElectronvoltThe energy gained by an electron moving through a potential difference of 1 V, 1.60 × 10−19 J.
Closest approachThe point where a charged particle momentarily stops and its kinetic energy has become potential energy.
Accelerating potential differenceThe voltage through which a charge gains kinetic energy qV.

Avoid these mistakes

1
Dropping the signs of the charges so attractive pairs seem to have positive energy.
2
Mixing up potential (V) with potential energy (qV).
3
Squaring the distance in the potential energy equation.
4
Converting eV to joules incorrectly — multiply by 1.60 × 10−19.
5
Applying ½mv2 = qV at relativistic speeds.

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