D.2 Electric and magnetic fields

UNIT SYLLABUS

SL/HL 8 hours SL + 6 hours HL

Coulomb's law is Newton's gravitation with two twists: charge replaces mass, and the force can repel as well as attract — because charge comes in two signs and is strictly conserved, as Millikan's oil drops showed in quantised units of $e$. The field picture carries over intact: field strength $E = F/q$, field lines from positive to negative, uniform fields between parallel plates ($E = V/d$). Magnetic fields join the family with their closed-loop field lines. At HL, electric potential mirrors its gravitational twin — but with both signs of charge, potentials can be positive or negative, and equipotential maps become the contour lines of electrostatics.

Guiding Questions

? How are electric and gravitational fields similar, and where do the analogies break down?
? What does the field model predict about charges placed in uniform and radial fields?

✓ What the IB expects you to master

Describe the two types of charge, the direction of forces between them, and conservation of charge.
Apply Coulomb's law $F = k\frac{q_1q_2}{r^2}$ with $k = \frac{1}{4\pi\varepsilon_0}$ for point charges.
Explain Millikan's experiment as evidence that charge is quantised in units of $e$ .
Describe charging by friction, electrostatic induction and contact, including grounding (earthing).
Use field strength $E = F/q$ , sketch field-line patterns, and relate line density to field strength.
Use the uniform field between parallel plates: $E = V/d$ .
Sketch magnetic field patterns (bar magnets, wires, coils) — field lines form closed loops.
HL: use electric potential energy $E_p = k\frac{q_1q_2}{r}$ and electric potential $V_e = \frac{kQ}{r}$ (zero at infinity).
HL: apply the potential gradient $E = -\Delta V_e/\Delta r$ and $W = q\Delta V_e$ , and map equipotential surfaces for electric fields.

1 Key Formulas

Coulomb's law

F = k\frac{q_{1}q_{2}}{r^{2}}

Coulomb constant

k = \frac{1}{4\pi\varepsilon_{0}}

Electric field strength

E = \frac{F}{q}

Uniform field (plates)

E = \frac{V}{d}

Electric PE (HL)

E_{p} = k\frac{q_{1}q_{2}}{r}

Electric potential (HL)

V_{e} = \frac{kQ}{r}

Potential gradient (HL)

E = -\frac{\Delta V_{e}}{\Delta r}

Work done (HL)

W = q\Delta V_{e}

2 Exam Preparation & Topic Explanations

Working the gravity–electricity dictionary

Every D.1 formula maps to a D.2 formula under $m \to q$ , $G \to k$ : learn them as one family, not two. The physics difference — repulsion exists, potentials can be positive — is exactly what examiners probe.

Field-line sketches earn marks with three rules: lines start on positive and end on negative charge (or infinity), never cross, and their density encodes strength.

Pro Exam Strategy

The sign of $E_p = kq_1q_2/r$ takes care of itself if you keep the charges' signs — positive means repulsive pair.
Between parallel plates the field is uniform: same force everywhere, parabolic projectile-like paths for moving charges.
Grounding removes surplus charge — describe electron flow direction explicitly.
Magnetic field lines are closed loops — no magnetic monopoles; a compass maps them.

3 MCQ Practice

Q1. Two point charges attract with force $F$ . If both charges are doubled and the separation halved, the force becomes:

$2F$
$4F$
$8F$
$16F$

Q2. In Millikan's experiment, every measured droplet charge was found to be:

Exactly equal to $e$
An integer multiple of $e$
Randomly distributed
Proportional to the droplet mass

Q3. A proton is released from rest in a uniform electric field. It moves:

Along a field line, from high to low potential
Along a field line, from low to high potential
Perpendicular to the field lines
Along an equipotential surface

4 Short Answer Questions

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