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Theme D — Fields

D.1.8 Gravitational Equipotential Surfaces — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 10 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.1.8 Gravitational Equipotential Surfaces — IB PHYSICS HL notes: Describe and draw gravitational equipotential surfaces for radial and uniform fields and explain why no work is done along them.Equipotential line — joins points of equal gravitational potential in two dimensionsEq…

  • Perpendicular
  • Direction of field
  • Near the Earth's surface
  • Along a line
  • Between lines
  • Spacing and strength

Section 1 of 9What an equipotential is

Equipotential line
  • Equipotential line joins points of equal gravitational potential in two dimensions
Equipotential surface
  • Equipotential surface the same in three dimensions
Drawing
  • Drawing dotted lines, whereas field lines are solid with arrows
No arrows
  • No arrows equipotentials have no direction and are not vectors

Section 2 of 9Link to field lines

Perpendicular
  • Perpendicular equipotentials always cross field lines at right angles in radial and uniform fields
Direction of field
  • Direction of field from higher to lower potential
Gradient
  • Gradient the potential gradient is defined by the equipotential lines

Section 3 of 9Radial field

Shape
  • Shape concentric circles around the planet
    • (spheres in three dimensions)
Spacing
  • Spacing they get further apart with distance from the planet
Reason
  • Reason the field strength falls with distance so the same potential change needs a bigger gap

Section 4 of 9Uniform field

Near the Earth's surface
  • Near the Earth's surface equipotentials are horizontal straight lines
Spacing
  • Spacing parallel and equally spaced
Reason
  • Reason the field has constant strength

Section 5 of 9Work along an equipotential

Along a line
  • Along a line no work is done because ΔV = 0
Energy
  • Energy an object moving along an equipotential neither gains nor loses energy
Between lines
  • Between lines work is done when moving between equipotentials, W = mΔV
Spacing and strength
  • Spacing and strength equipotentials closer together mean a stronger field

Section 6 of 9Drawing rules

Straight lines
  • Straight lines use a ruler for uniform fields
Circles
  • Circles draw concentric circles for point masses
Right angles
  • Right angles cross the field lines at 90°
Labels
  • Labels label potential values when given

Section 7 of 9More from the specification

1Equipotential spatial mapping
  • Equipotential spatial mapping tracing lines of identical gravitational potential perpendicular to field lines provides a graphic means to visualize conservative fields.
2Newton's Law of Universal Gravitation
  • The attractive gravitational force between two point masses M and m separated by distance r is given by Newton's law: F = G*M*m / r², directed towards the centre of mass.
3Orbital Speed of a Satellite
  • For a satellite in a circular orbit of radius r around a planet of mass M, the gravitational force provides the centripetal force, yielding orbital speed v = √(G*M / r).
    • (G*M*m / r² = m*v² / r)
4Kepler's Third Law and Orbital Period
  • Equating orbital speed to 2πr / T leads to Kepler's third law equation T² = (4π² / GM) * r³, showing that the square of orbital period T is directly proportional to the cube of orbital radius r.
5Gravitational Potential and Escape Speed
  • Gravitational potential Vg = -GM/r represents the work done per unit mass in bringing a body from infinity;
    • the minimum escape speed required to break free from a planet's surface is vesc = √(2GM / R).
6Escape speed
  • Minimum launch speed to reach infinity, √(2GM/R).
7Centripetal force
  • Net force toward the centre, mv2/r.
8Escape velocity
  • Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
9Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
10Radius
  • Distance from the centre to the circular path.
11Period
  • Time for one revolution.
12Newton
  • Unit of force, kg m s-2.
13Density
  • Mass per unit volume.
14Gravitational force
  • Attractive force between masses.
15Orbital period
  • Time for one orbit.
16Kinetic energy
  • K = ½mv2, energy of motion.

Section 8 of 9Key terms

TermMeaning
Equipotential surfaceA surface on which the gravitational potential is the same at every point.
Radial fieldA field whose lines point to the centre of a sphere.
Uniform fieldA field with constant strength and direction, drawn with parallel equally spaced lines.
Potential differenceThe change in potential between two equipotentials.

Section 9 of 9Exam technique

1
Drawing equipotentials with arrows.
2
Drawing equipotentials parallel to field lines instead of perpendicular.
3
Saying work is needed to move along an equipotential — none is needed.
4
Drawing equally spaced equipotentials for a radial field — they get further apart.
5
Saying equipotentials are vectors.

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