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D.2.10 Electric Equipotential Surfaces — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 25 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.2.10 Electric Equipotential Surfaces — IB PHYSICS HL notes: Describe and sketch electric equipotential surfaces for point charges, dipoles, conductors and parallel plates and relate their spacing to field strength.Definition — lines (2D) or surfaces (3D) of equal electric poten…

  • Contour analogy
  • Never cross
  • Perpendicular
  • Potential gradient
  • Near the charge
  • Charged conducting sphere

Part 1 of 8Equipotential surfaces

Definition
  • Definition lines (2D) or surfaces (3D) of equal electric potential
Contour analogy
  • Contour analogy they act like contour lines on a map
Work
  • Work none is done moving a charge along one because W = qΔV = 0, so its potential energy does not change
Drawing
  • Drawing dotted or plain lines without arrows because they are not vectors
Never cross
  • Never cross a point cannot have two potentials

Part 2 of 8Link to field lines

Perpendicular
  • Perpendicular equipotentials always cross field lines at right angles
Reason
  • Reason a field component along a surface would push a charge along it and change its potential energy
Direction
  • Direction the field points from higher to lower potential, across the surfaces
Potential gradient
  • Potential gradient equipotential lines represent the gradient

Part 3 of 8Point charge and charged sphere

1Shape
  • Shape concentric circles around the charge, radius r = kQ/V
    • (spheres in three dimensions)
2Spacing
  • Spacing they get further apart with distance because the field falls
3Near the charge
  • Near the charge lines get closer together as the potential gradient steepens
  • More work is needed to push a positive test charge gradually closer
4Charged conducting sphere
  • Charged conducting sphere the same pattern as a point charge

Part 4 of 8Multiple charges

Dipole
  • Dipole curved surfaces with a central line at 0 V where the opposing potentials cancel
Like charges
  • Like charges surfaces around each charge close in, merging into one surface around both
  • A region of empty space between them marks where the resultant field is zero
Method
  • Method draw curves perpendicular to the field lines
Greatest potential
  • Greatest potential near the charges, decreasing with distance
Unequal charges
  • Unequal charges the larger charge has more field lines and a bigger sphere of influence
  • The zero-field point lies closer to the smaller charge

Part 5 of 8Parallel plates

Uniform field
  • Uniform field horizontal straight lines that are parallel and equally spaced
Perpendicular
  • Perpendicular they cross the uniform field lines at 90°
Midway
  • Midway the potential is halfway between that of the plates

Part 6 of 8Spacing and field strength

Spacing and field strength
Relation
  • Relation for equal potential steps, Δr = ΔV/E
Close together
  • Close together a strong field
Far apart
  • Far apart a weak field
Estimating
  • E between two adjacent surfaces is the potential difference divided by the gap
Sharp points
  • Sharp points the surfaces crowd together near a sharp point on a conductor, showing a very strong field

Part 7 of 8Conductors

Surface
  • Surface a conductor in electrostatic equilibrium is an equipotential
Field lines
  • Field lines they meet the surface at 90°
Interior
  • Interior at one potential everywhere with no field
Earth
  • Earth the zero-potential reference, so a conductor connected to it is at 0 V

Part 8 of 8More from the specification

1Equipotential lines in electric and magnetic fields
  • Equipotential lines in electric and magnetic fields static electric fields perpendicular to equipotentials produce zero work,
    • whereas perpendicular magnetic fields deflect charges.
2Coulomb's Law and Electrostatic Force
  • Coulomb's law equation states that the magnitude of electrostatic force between two point charges is F = (1 / 4πε₀) · (|q₁q₂| / r²),
  • where ε₀ represents the permittivity constant of free space;
    • positive and negative charges attract while like charges repel.
3Electric Potential and Equipotential Surfaces
  • An equipotential surface connects points of equal electric potential V = q / (4πε₀r);
  • because the potential difference between any two points on the surface is zero, no work is done moving a charge along it,
  • and field lines cross equipotentials at right angles.
4Potential Gradient and Moving Charge Comparison
  • On an electric potential graph against distance, the negative potential gradient equals the electric field strength (E = -dV/dr);
    • in comparison, electric current flowing through conductors creates circular magnetic field lines whose forces depend on charge velocity.
5Coulomb's Law and Electrostatic Force
  • Coulomb's law equation states that the magnitude of electrostatic force between two point charges is F = (1 / 4πε₀) · (|q₁q₂| / r²),
  • where ε₀ represents the permittivity constant of free space;
    • positive and negative charges attract while like charges repel.
6Electric Potential and Equipotential Surfaces
  • An equipotential surface connects points of equal electric potential V = q / (4πε₀r);
  • because the potential difference between any two points on the surface is zero, no work is done moving a charge along it,
  • and field lines cross equipotentials at right angles.
7Potential Gradient and Moving Charge Comparison
  • On an electric potential graph against distance, the negative potential gradient equals the electric field strength (E = -dV/dr);
    • in comparison, electric current flowing through conductors creates circular magnetic field lines whose forces depend on charge velocity.
8Coulomb
  • Charge passing a point when a current of 1 A flows for 1 s.
9Permittivity
  • A property of a medium affecting the electric force within it.
10Constant
  • Not changing.
11Current
  • Flow of electrons in a circuit.
12Density
  • Mass per unit volume.
13Force
  • A push or pull measured in newtons.
14Magnetic field
  • Area around a magnet where its effects can be detected.
15Relative permittivity
  • Ratio of the permittivity of a material to that of free space.
16W = 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
Equipotential surfaceA surface on which every point is at the same electric potential.
Contour analogyLines of equal height on a map correspond to lines of equal potential.
PerpendicularityEquipotentials meet field lines at 90°.
SpacingThe separation ΔV/E for equal potential steps.
Conductor surfaceAn equipotential in electrostatic equilibrium.

Avoid these mistakes

1
Drawing equipotentials parallel to the field lines.
2
Thinking work is needed to move a charge along an equipotential.
3
Allowing equipotentials to cross.
4
Drawing equally spaced equipotentials for a radial field — they spread out with distance.
5
Forgetting that around a negative charge the potentials are negative.

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