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Theme D — Fields

Theme D — Fields — IB Physics HL Revision Notes & Topical Questions

10 min read 12 parts Lesson 1 of 39 Unit 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

Theme D — Fields — IB PHYSICS HL notes: Summarise gravitational, electric and magnetic fields, potential, orbits, Coulomb's law, forces on moving charges and Millikan's experiment for IB Physics HL.Newton's law — the force between two point masses is proportional to the product o…

  • Field strength
  • Uniform field
  • Line density
  • Laboratory heights
  • Neutral point
  • Potential energy

Part 1 of 9Newton's law of gravitation and field strength

Newton's law
  • Newton's law the force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation
  • F = Gm1m2/r2 with r measured between centres
Point masses
  • Point masses planets and stars are treated as point masses because their separation is much greater than their radii
Direction
  • Direction gravitational forces are always attractive
Field strength
  • Field strength g = F/m = GM/r2 in N kg−1, equal to the acceleration of free fall
Weight
  • W = mg so weight changes from place to place while mass does not
  • On the Moon g is about 1.6 N kg−1
Changes
  • Changes use ratios such as F ∝ 1/r2 and g ∝ M/r2

Part 2 of 9Gravitational field lines

Point mass
  • Point mass field lines are radial and point inwards, and the field is non-uniform because g changes with distance
Uniform field
  • Uniform field parallel equally spaced lines near a planet's surface
Line density
  • Line density the number of lines through a sphere of area 4πr2 falls as 1/r2 so spacing shows magnitude and arrows show direction
Laboratory heights
  • Δg ≈ −2gΔr/R is only a few parts per million so the field is effectively uniform
Neutral point
  • Neutral point between masses M and M′ a distance d apart, GM/x2 = GM′/(d − x)2 gives x/(d − x) = √(M/M′)

Part 3 of 9Gravitational potential, energy and equipotentials

Gravitational potential, energy and equipotentials
Potential
  • Potential the work done per unit mass by an external agent bringing a small mass from infinity to the point
  • V = −GM/r in J kg−1
Scalar
  • Scalar it is zero at infinity and negative because gravity is attractive
  • Closer to a planet the potential is more negative
Potential energy
  • Ep = mV = −GMm/r
  • ΔEp = mΔV, positive moving away and negative falling towards the body
Stored in
  • Stored in the system of both masses
Work
  • W = mΔV
Equipotential surfaces
  • Equipotential surfaces perpendicular to field lines
  • They are closer together where the field is stronger
Direction
  • Direction the field points from higher to lower potential
Along an equipotential
  • Along an equipotential no work is done
Gradient
  • Gradient g = −ΔV/Δr

Part 4 of 9Escape speed and orbits

Escape speed
  • Escape speed the minimum launch speed to reach infinity with zero speed, ignoring air resistance and other bodies
  • It does not depend on the launch direction or on the projectile's mass
Equation
  • ½mv2 = GMm/r gives vesc = √(2GM/r)
Circular orbit
  • Circular orbit gravity supplies the centripetal force so v = √(GM/r)
  • T2 ∝ r3 (Kepler's third law)
Orbital energy
  • Orbital energy total energy is −GMm/2r
Geostationary orbit
  • Geostationary orbit above the equator with a 24 h period
Weightlessness
  • Weightlessness astronauts are in free fall, not in zero gravity
  • At 400 km g is still about 8.7 N kg−1, 89% of the surface value

Part 5 of 9Charge and Coulomb's law

Charge
  • Charge quantised in units of e = 1.60 × 10−19 C and conserved
Conservation
  • Conservation nuclear decay also conserves charge, as in n → p+ + e− + antineutrino
Coulomb's law
  • F = kq1q2/r2
    What the symbols mean: F = electric force (N) · Q1, Q2 = charges (C) · r = separation (m) · k = 1/4πε0 = 8.99 × 109 N m2 C−2
  • k = 1/(4πε0) = 8.99 × 109 N m2 C−2 in a vacuum with ε0 = 8.85 × 10−12 C2 N−1 m−2
Media
  • Media air is treated like a vacuum and other materials have higher permittivity so k is smaller
Compared with gravity
  • Compared with gravity electric forces can be attractive (unlike charges) or repulsive (like charges)

Part 6 of 9Electric field strength

Electric field strength
Definition
  • E = F/q, the force per unit positive charge, in N C−1
    What the symbols mean: E = electric field strength (N C−1) · F = force on the charge (N) · Q or q = charge (C)
Point charge
  • E = kQ/r2
Parallel plates
  • Parallel plates a uniform field E = V/d
Field lines
  • Field lines from positive to negative, radial for a point charge and parallel where they meet a flat plate
Charged particle in a uniform field
  • Charged particle in a uniform field a constant force gives a parabolic path for perpendicular entry
  • A positive particle moves towards the negative plate and a negative one towards the positive plate
Neutron
  • Neutron it is undeflected
Mass
  • Mass deflection is smaller for greater mass
Charge-to-mass ratio
  • Charge-to-mass ratio q/m is 1.76 × 1011 C kg−1 for an electron and 9.58 × 107 C kg−1 for a proton

Part 7 of 9Electric potential, energy and gradient

Potential
  • V = kQ/r is a scalar, zero at infinity, positive near a positive charge and negative near a negative charge
Several charges
  • Several charges add the potentials algebraically
  • At the midpoint of a dipole V = 0 although the field is not zero
Work
  • W = qΔV and for a point charge ΔV = kQ(1/rf − 1/ri)
  • The path does not matter because the field is conservative
Potential energy
  • Ep = kq1q2/r
  • Positive for like charges and negative for unlike charges, equal to the area under the F–r graph from r to infinity
Gradient
  • E = −ΔV/Δr
  • The V–r graph of a point charge is 1/r shaped and the E–r graph follows 1/r2
Area
  • Area the area under an E–r graph is the change in potential
Equipotentials
  • Equipotentials they crowd together close to a point charge

Part 8 of 9Magnetic forces on currents and moving charges

1Current in a field
  • F = BIL sin θ
    What the symbols mean: F = force on the wire (N) · B = magnetic flux density (T) · I = current (A) · L = length of wire in the field (m) · θ = angle between wire and field
  • It is greatest (BIL) when the current is perpendicular to the field and zero when parallel
2Direction
  • F, B and I are mutually perpendicular, given by the left-hand rule using conventional current
3Moving charge
  • F = qvB sin θ, perpendicular to the velocity
  • It does no work, so the particle moves in a circle of radius r = mv/Bq
4Charge-to-mass ratio
  • Charge-to-mass ratio q/m = v/(rB)
5Velocity selector
  • Velocity selector perpendicular E and B fields pass only v = E/B = V/(Bd)
  • This gives q/m = V/(rB2d) in J. J. Thomson's method
6Negative charge
  • Negative charge the force is in the opposite direction to that on a positive charge
7Force
  • F/L = μ0I1I2/2πr
8Same direction
  • Same direction the wires attract
9Opposite directions
  • Opposite directions the wires repel
10Field zero point
  • Field zero point between parallel currents where I1/r1 = I2/r2
  • For antiparallel currents it lies outside the pair, nearer the smaller current

Part 9 of 9More from the specification

More from the specification
Earth's Gravitational Field and Surface Acceleration
  • The gravitational field strength at or near the Earth's surface depends on Earth's mass ME and Earth radius RE ; gravitational force on an object decreases with the square of distance from Earth's centre.
    • (g = G·ME / RE² ≈ 9.81 N·kg⁻¹)
Satellite Orbital Motion and Kinetic Energy
  • In stable circular orbital motion of a satellite around Earth, centripetal force is provided by gravity, yielding orbital kinetic energy Ek = ½·m·v² = G·ME·m / (2r); decreasing orbital radius increases satellite velocity and kinetic energy.
    • (G·ME·m / r² = m·v² / r)
Gravitational Potential Energy and Total Orbital Energy
  • Gravitational potential energy of an object at distance r from Earth is Ep = -G·ME·m / r;
    • moving an object into a higher orbit increases total orbital mechanical energy (Etotal = -G·ME·m / (2r)),
  • which means external work must be supplied.
Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
Kinetic energy
  • K = ½mv2, energy of motion.

Key terms

TermMeaning
Gravitational field strengthThe force per unit mass at a point in a gravitational field, g = GM/r2.
Gravitational potentialThe work done per unit mass in bringing a mass from infinity to a point, V = −GM/r.
Escape speedThe minimum launch speed needed to reach infinity with zero speed.
Coulomb's lawThe force between two point charges is F = kq1q2/r2.
EquipotentialA surface on which every point has the same potential.
Charge-to-mass ratioThe charge of a particle divided by its mass, q/m.
Quantised chargeCharge exists only in whole-number multiples of e = 1.60 × 10−19 C.
Geostationary orbitAn equatorial orbit with a 24 h period that keeps a satellite above one point.

Avoid these mistakes

1
Using the distance between surfaces instead of centre-to-centre distance in F = Gm1m2/r2.
2
Treating potential as a vector or forgetting its sign — it is a scalar and gravitational potential is negative.
3
Thinking astronauts are weightless because gravity is zero — they are in free fall with gravity still about 89% of its surface value.
4
Reversing the deflection direction for a negative charge or misusing the left-hand rule.
5
Assuming the electric field is zero where the potential is zero, for example at the midpoint of a dipole.

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