Electromagnetism
What the Exam Tests
The syllabus lists four topics: electrostatics (Coulomb's law, electric field strength, electric potential), direct-current circuits (Ohm's law, series and parallel circuits), the magnetic field (magnetic induction, Ampère's force, the Lorentz force) and electromagnetic induction (Faraday's law, Lenz's law).
Questions can show field lines and equipotentials, a circuit whose rheostat slider moves, a charged particle curving in a magnetic field, or a rod sliding on rails, and ask for a force, a current, a direction, or how a meter reading changes.
In our mock papers Electromagnetism gets 13 of the 48 questions. The CSCA publishes the topics but not how many questions each gets, so this split is our own reading of the syllabus. The AC Circuits lesson (alternating current, transformers, LC circuits) and the Biot–Savart law go beyond the syllabus: they are marked in practice and left out of mocks.
Electric Charge
There are two types of electric charge: positive and negative. Like charges repel; opposite charges attract. Charge is quantised – it comes in multiples of the elementary charge e = 1.6×10⁻¹⁹ C. Charge is also conserved: the total charge in an isolated system never changes.
Coulomb’s Law
The force between two stationary point charges in vacuum (库仑定律, Coulomb’s law) is: F = kq₁q₂/r², where k = 9×10⁹ N·m²/C². Substitute the magnitudes of the charges and decide the direction separately. The elementary charge e is called 元电荷 in Chinese. The force is along the line joining the charges. It is attractive for opposite charges and repulsive for like charges. Doubling the distance reduces the force by a factor of 4. The law applies to point charges (点电荷): charged bodies whose size is negligible compared with their separation.
Charging and Sharing Charge
Bodies are charged by friction (摩擦起电), by contact (接触起电) or by induction (感应起电). None of these creates charge; each only moves electrons from one place to another. When two identical metal spheres touch, the total charge is shared equally, so each ends with (q₁ + q₂)/2, signs included. Example: spheres carrying +5Q and −Q touch and are put back at the same distance r. Each now has +2Q, so the force changes from 5kQ²/r² (attractive) to 4kQ²/r² (repulsive), 4/5 of the original size.
Superposition
When multiple charges are present, the net force on any charge is the vector sum of individual Coulomb forces. Break into x and y components, sum separately, then combine.
Key takeaway: F = kq₁q₂/r². Charge is quantised and conserved. Use vector superposition for multiple charges.
Key Formulas
- F = kq₁q₂/r², k = 9×10⁹
- e = 1.6×10⁻¹⁹ C
Worked Example 1
Q: Two charges +3µC and −5µC are 0.2 m apart. Find the force.
A: F = 9×10⁹ × 3×10⁻⁶ × 5×10⁻⁶ / (0.2)² = 3.375 N (attractive).
Worked Example 2
Q: Three charges in a line: +2µC at origin, −4µC at x=0.1 m, +1µC at x=0.3 m. Find net force on the middle charge.
A: F₁₂ = k(2)(4)×10⁻¹²/(0.1)² = 7.2 N left. F₃₂ = k(4)(1)×10⁻¹²/(0.2)² = 0.9 N right. Net = 6.3 N left.
Worked Example 3
Q: How many excess electrons give a charge of −3.2×10⁻¹⁸ C?
A: n = Q/e = 3.2×10⁻¹⁸/1.6×10⁻¹⁹ = 20 electrons.
Exam tip: Always convert µC to C.
Exam tip: Check sign: opposite charges → attractive.
Exam tip: Use components for 2D problems.
Common mistake: Forgetting to square the distance.
Common mistake: Not converting micro-coulombs to coulombs.
Common mistake: Ignoring vector directions.
Try This Yourself
Module Summary
Open and read all sections to complete this module