Electricity and magnetism is not one topic. It is four topics that the DBE spreads across Paper 1 and together they carry over 80 marks.
Electrostatics. Electric circuits. Electromagnetic induction. Motors and generators.
Most students study these as separate chapters and never connect them. But they are all part of the same story: charges, forces, fields, and what happens when you move charges through magnetic fields.
This post puts it all in one place. Every formula. Every rule. Every comparison table. One reference to rule them all.
In This Post You Will Learn
✓ Every formula you need for electrostatics, circuits, and electrodynamics in one place
✓ The key differences between electrostatics and current electricity
✓ How Coulomb's Law, electric fields, and potential difference connect
✓ The complete circuit rules for series, parallel, and internal resistance
✓ How generators, motors, and Faraday's Law tie together
✓ Quick reference tables you can use during revision
Part 1: Electrostatics
Electrostatics deals with stationary charges. No current flows. Just charges sitting there exerting forces on each other.
Coulomb's Law
The force between two point charges:
F = kQ₁Q₂ / r²
k = 9 x 10⁹ N.m²/C²
Q = charge in coulombs (C)
r = distance between charges in metres (m)Positive force = repulsion (same sign charges).
Negative force = attraction (opposite sign charges).
This is an inverse square law. Double the distance and the force drops to a quarter. Triple the distance, the force drops to a ninth. The exam loves asking what happens when you change r.
Electric Field
An electric field is the region around a charge where another charge would experience a force.
E = F/q = kQ/r²
E = electric field strength (N/C or V/m)
F = force on test charge (N)
q = test charge (C)
Q = source charge (C)
r = distance from source charge (m)Direction of electric field lines:
| Charge Type | Field Direction |
|------------|-------------------------|
| Positive | Away from the charge |
| Negative | Towards the charge |Field lines never cross. They start on positive charges and end on negative charges.
Electric Field Between Parallel Plates
E = V/d
V = potential difference between plates (V)
d = distance between plates (m)This gives a uniform field (equal strength everywhere between the plates). The field lines are parallel and evenly spaced.
Work Done on a Charge
W = qV or W = Fd or W = qEd
W = work done (J)
q = charge (C)
V = potential difference (V)Key connection: Potential difference (voltage) is the work done per unit charge. V = W/q. This links electrostatics to circuits.
Part 2: Electric Circuits
Current electricity deals with charges that are moving through conductors.
Ohm's Law
V = IR
V = potential difference (V)
I = current (A)
R = resistance (Ω)Series Circuit Rules
| Property | Rule |
|------------|-------------------------------|
| Current | Same through all components |
| Voltage | Splits between components |
| Resistance | R_total = R₁ + R₂ + R₃ |Parallel Circuit Rules
| Property | Rule |
|------------|-------------------------------|
| Voltage | Same across all branches |
| Current | Splits between branches |
| Resistance | 1/R_total = 1/R₁ + 1/R₂ |Shortcut for two resistors in parallel:
R_total = (R₁ x R₂) / (R₁ + R₂)
Internal Resistance and EMF
EMF (ε) = total voltage the battery produces
Terminal voltage = voltage available to external circuit
ε = V_external + V_internal
ε = I(R + r)
V_terminal = ε - Ir
"Lost volts" = Ir (wasted as heat inside battery)Power in Circuits
P = VI = I²R = V²/R
P = power (W)
Energy = Pt (in joules)We covered circuits in full detail in Electric Circuits Grade 12 - Parallel and Series Explained.
Part 3: Electrodynamics (Motors and Generators)
This is where electricity and magnetism combine. Moving charges in magnetic fields. Spinning coils. Induced currents.
The Motor Effect
A current-carrying conductor in a magnetic field experiences a force.
F = BIL sinθ
F = force (N)
B = magnetic field strength (T)
I = current (A)
L = length of conductor in field (m)
θ = angle between conductor and fieldWhen θ = 90° (perpendicular), force is maximum. When θ = 0° (parallel), force is zero.
This is how a motor works. Current goes in, the coil spins.
Faraday's Law (Electromagnetic Induction)
A changing magnetic flux through a coil induces an EMF.
ε = -NΔΦ/Δt
ε = induced EMF (V)
N = number of turns
ΔΦ = change in magnetic flux (Wb)
Δt = time for the change (s)
Magnetic flux: Φ = BA cosθ
B = magnetic field (T)
A = area of coil (m²)
θ = angle between field and normal to coilThis is how a generator works. The coil spins, EMF comes out.
Lenz's Law
The induced current flows in a direction that opposes the change that caused it.
The system fights back. Push a magnet in, the coil pushes it out. Pull it away, the coil tries to hold it. Nature resists change.
Generators vs Motors
| Feature | Generator | Motor |
|-----------------|---------------------------|---------------------------|
| Energy in | Mechanical (spin the coil) | Electrical (current in) |
| Energy out | Electrical (EMF produced) | Mechanical (coil spins) |
| Principle | Faraday's Law | Motor effect (F = BIL) |
| AC version uses | Slip rings | Split-ring commutator |
| DC version uses | Split-ring commutator | Split-ring commutator |AC vs DC Generator
| Feature | AC Generator | DC Generator |
|---------------------|--------------------|-----------------------|
| Output | Alternating current | Direct current (bumpy) |
| Commutator type | Slip rings | Split-ring commutator |
| Output graph | Sine wave | Pulsating positive wave|
| Current direction | Reverses each half turn | Always same direction |How to Increase Induced EMF
From the formula ε = NΔΦ/Δt:
✓ More turns (increase N)
✓ Stronger magnet (increase B, which increases ΔΦ)
✓ Larger coil area (increase A, which increases ΔΦ)
✓ Spin faster (decrease Δt)We covered this in detail in Electromagnetic Induction Grade 12 - Generators and Motors Explained.
Part 4: The Master Formula Sheet
Every formula you need for electricity and magnetism in one place.
Electrostatics
Coulomb's Law: F = kQ₁Q₂/r² (k = 9 x 10⁹)
Electric field: E = F/q = kQ/r²
Field between plates: E = V/d
Work done: W = qV = qEd = Fd
Potential difference: V = W/qCircuits
Ohm's Law: V = IR
Series R: R_T = R₁ + R₂ + R₃
Parallel R: 1/R_T = 1/R₁ + 1/R₂
EMF equation: ε = I(R + r)
Terminal voltage: V = ε - Ir
Power: P = VI = I²R = V²/R
Energy: E = Pt = VItElectrodynamics
Motor effect: F = BIL sinθ
Magnetic flux: Φ = BA cosθ
Faraday's Law: ε = -NΔΦ/ΔtHow the Marks Are Spread Across Paper 1
| Topic | Marks | Questions |
|-----------------------------|--------|-------------|
| Electrostatics | 10-15 | Q2-3 |
| Electric circuits | 50-55 | Q8-9 |
| Electromagnetic induction | 15-20 | Q10-11 |
| TOTAL ELECTRICITY + MAGNETISM | 80-90 | |That is more than half of Paper 1 from electricity and magnetism topics alone.
For full live lessons on all of these topics, see our Grade 12 Physical Science tuition page.
Common Mistakes Students Make
- Confusing E = kQ/r² with E = V/d
The first formula is for the electric field around a point charge. The second is for the uniform field between parallel plates. Students use them interchangeably. They are not the same thing. Check what type of field the question describes.
- Forgetting internal resistance in circuit calculations
When the question gives r (internal resistance), your total R is R_external + r. Leaving out r gives wrong current, which ruins every calculation after it.
- Confusing slip rings with split-ring commutator
Slip rings = AC generator. Split-ring commutator = DC generator and motors. Swapping them in the exam loses you the marks.
- Thinking maximum flux means maximum EMF
Maximum flux is when the coil is perpendicular to the field. But EMF depends on the rate of CHANGE of flux. Maximum EMF happens when flux is changing fastest, which is when it passes through zero. This is counterintuitive and students get it wrong every year.
- Not stating direction in electrostatics answers
Force and electric field are vectors. You must state direction. "The force is 0.5 N" is incomplete. "The force is 0.5 N to the right (attractive)" is complete.
- Using the wrong sign convention in Coulomb's Law
If both charges are positive, the force is positive (repulsive). If one is positive and one negative, the force is negative (attractive). Students assign charge signs randomly. Read the question carefully.
How to Use This Cheat Sheet
Print this post or keep it open on your phone while you study.
When you do a past paper question on electricity or magnetism:
Step 1: Identify which sub-topic it is (electrostatics, circuits, or electrodynamics).
Step 2: Find the relevant formula from the master sheet above.
Step 3: Check units before substituting.
Step 4: Solve and include direction for vector quantities.
For common errors to avoid across all of Physical Science, read 10 Most Common Mistakes in Grade 12 Physical Science.
Want live lessons covering electricity, magnetism, and every Paper 1 topic?
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