This mini-lesson covers Themes D.1–D.3 — Fields: gravitational fields and Newton's law, electric fields and Coulomb's law, magnetic fields, and the motion of charges in electric and magnetic fields.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.
D.1 · gravity
Gravitational fields
A field is a region where a mass or charge feels a force. Gravitational field strength g is the force per unit mass. Newton's law of gravitation and the field of a point/spherical mass are inverse-square:
F = GMm ÷ r² · g = F ÷ m = GM ÷ r²G = 6.67 × 10⁻¹¹ N m² kg⁻²
Gravity is always attractive and acts on mass. Because g ∝ 1/r², doubling the distance from a planet's centre quarters the field strength.
Quick check
Quick check
?At the surface of a planet the gravitational field strength is g. What is it at a distance of two planet-radii from the centre?
Calculate
Calculate
#Find the gravitational field strength at Earth's surface. Use M = 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹.
Electric field strength E is the force per unit positive charge. Coulomb's law gives the force between point charges, and a point charge produces a radial field:
F = kQ₁Q₂ ÷ r² · E = F ÷ q = kQ ÷ r²k = 8.99 × 10⁹ N m² C⁻²
Unlike gravity, electric forces can attract or repel: like charges repel, unlike attract. Field lines point away from positive charge and towards negative.
Calculate
Calculate
#Two charges, 3.0 µC and 2.0 µC, are 0.10 m apart. Find the electrostatic force between them. (k = 8.99 × 10⁹.)
#A charge of 2.0 µC feels a force of 6.0 mN (6.0 × 10⁻³ N) in an electric field. Find the field strength.
N C⁻¹
Hint: E = F ÷ q = 6.0e-3 ÷ 2.0e-6.
D.2–D.3 · magnetic
Magnetic fields & forces
A magnetic field exerts a force on a moving charge or a current. The force is perpendicular to both the field and the velocity/current (Fleming's left-hand rule):
F = BIL · F = qvBwire of length L carrying current I · charge q moving at speed v
Because the magnetic force on a moving charge is always perpendicular to its velocity, it does no work — it changes direction, not speed, making charges move in circles.
Calculate
Calculate
#A 0.20 m wire carries 5.0 A at right angles to a 0.40 T magnetic field. Find the force on it.
N
Hint: F = BIL = 0.40 × 5.0 × 0.20.
Quick check
Quick check
?A magnetic field does no work on a charged particle moving through it. Why?
Sort it
Which field does this describe?
Tap an item, then tap the group it belongs to.
🌍 Gravitational
⚡ Electric
🧲 Magnetic
Match it
Match the law to its equation
Tap a statement on the left, then its match on the right.
Statement
Answer
D.1 · HL depth
Potential, energy & orbits
At HL fields are described by potential — the potential energy per unit mass or charge. For a point mass and point charge:
V_g = −GM ÷ r · V_e = kQ ÷ rfield strength is the negative gradient of potential
Gravitational potential energy E_P = −GMm/r. The escape speed (KE just enough to reach r → ∞) and a circular orbital speed are:
v_escape = √(2GM ÷ r) · v_orbit = √(GM ÷ r)a bound orbit has total energy E = −GMm ÷ 2r
Gravitational potential is always negative and rises to zero at infinity; you must do positive work to lift a mass away.
Calculate
Calculate
#HL: find the escape speed from Earth's surface, in km s⁻¹. Use M = 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m.
km s⁻¹
Hint: v = √(2GM ÷ r) = √(2 × 6.67e-11 × 5.97e24 ÷ 6.37e6), then ÷1000.
Calculate
Calculate
#HL: find the orbital speed of a satellite at radius 7.0 × 10⁶ m from Earth's centre, in km s⁻¹.
km s⁻¹
Hint: v = √(GM ÷ r) = √(6.67e-11 × 5.97e24 ÷ 7.0e6), then ÷1000.
Recap
The big ideas to know
Gravitational: g = GM/r²; F = GMm/r²; attractive, acts on mass
Electric: E = kQ/r²; F = kQ₁Q₂/r²; attracts or repels
Magnetic: F = BIL and F = qvB; force ⟂ velocity, so does no work
Inverse square: doubling r quarters both gravitational and electric field
HL: potential V = −GM/r (grav) or kQ/r; v_escape = √(2GM/r)
That completes Fields for IB Diploma Physics HL. Press Finish to see your score.
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