A-Level Physics: Electromagnetic Forces Guide
Download printable cheat-sheet (CC-BY 4.0)14 Jul 2025, 00:00 Z
TL;DR
Magnetic fields are everywhere current flows. Mastering the three \(B\)-formulae, Fleming's rule and the Lorentz force lifts marks in Paper 2 calculation tricks and Paper 4 practicals. This guide turns the SEAB bullet-points into parent-approved check-lists, mini-drills and WA timing hacks.
1 What counts as a magnetic field?
A magnetic field is a region of space where a moving charge or a current-carrying conductor experiences a force. In the H2 syllabus it is treated as a vector field of force produced by currents or permanent magnets.
2 Field patterns produced by currents
2.1 Long straight wire
Field lines form concentric circles centred on the wire. The magnitude falls off with radial distance \(d\) according to
\[ B = \frac{\mu_0 I}{2 \pi d}. \tag{2.1} \]
Equation (2.1) can be derived via Ampère's law or the Biot-Savart law.
2.2 Flat circular coil (\(N\) turns, radius \(r\))
Near the centre the field is approximately uniform and given by
\[ B = \frac{\mu_0 N I}{2 r}. \tag{2.2} \]
A quick way to remember: halve the solenoid result, replace length with diameter.
2.3 Long solenoid (\(n=N/L\) turns per metre)
Inside a tightly wound solenoid the field is nearly uniform:
\[ B = \u_0 n I. \tag{2.3} \]
Inserting a ferrous core (iron) multiplies \(B\) by the material 's relative permeability \(\mu_r\)—the working principle of electromagnets used in MRI machines.
Mini-drill
Predict the shape of the field outside a solenoid. (Answer: similar to a bar magnet—closed loops emerging from one end and re-entering the other.)
3 Force on a current-carrying conductor
3.1 Core equation and direction
When a conductor of length \(l\) carrying current \(I\) sits in an external field \(B\), the magnetic (Lorentz) force is
\[ F = B I l \sin \theta, \tag{3.1} \]
with direction given by Fleming's left-hand rule.
3.2 Defining magnetic flux density
Re-arranging (3.1) for perpendicular orientation \((\theta = 90^{\circ})\) gives
\[ B = \frac{F}{I l}. \tag{3.2} \]
Hence magnetic flux density is “force per unit current per unit length.”
3.3 Measuring \(B\) with a current balance
Suspend the test conductor on a sensitive balance, run a known \(I\) and record the mass difference \(\Delta m\). From \(F = \Delta m g\) and (3.2) deduce \(B\).
3.4 Parallel-wire interactions
Two long, parallel wires carrying currents \(I_1\) and \(I_2\) a distance \(r\) apart exert equal and opposite forces
\[ \frac{F}{l} = \frac{\mu_0 I_1 I_2}{2 \pi r}. \tag{3.3} \]
Currents in the same direction attract; opposite directions repel—an idea embedded in the SI definition of the ampere.
4 Force on an isolated moving charge
4.1 Lorentz force
A charge \(Q\) entering a uniform field with speed \(v\) feels
\[ F = B Q v \sin \theta. \tag{4.1} \]
The force is always perpendicular to both \(\vec{v}\) and \(\vec{B}\), producing circular or helical motion.
4.2 Uniform circular motion
For \(\pu{\theta = 90^\circ}\) the radius is
\[ r = \frac{m v}{Q B}. \tag{4.2} \]
This relationship underpins the mass spectrometer.
5 Crossed fields and velocity selection
Set up perpendicular electric \(E\)- and magnetic \(B\)-fields such that \(Q E = Q v B\). Only particles with
\[ v = \frac{E}{B} \tag{5.1} \]
exit undeflected—perfect for ion-implantation or cathode-ray oscilloscopes.
6 IP-style study hacks
| Weak spot | Quick fix |
| Forgetting which rule (left vs right hand) | Write “FBI” on your lab glove: Force, B-field, I current direction. |
| Mixing up the three \(B\) equations | Create a flash-card: “Wire → \(2 \pi d\), Coil → \(2r\), Solenoid → \(n\).” |
| Sign errors in crossed-field Qs | Pre-draw axis arrows and annotate charge sign before any algebra. |
6.1 Why parents should care
IP schools allot fewer contact hours for classical electromagnetism, banking on student independence. Targeted tuition bridges the gap with timed drilling and data-logger labs, preventing the common Term 3 “dip” before promos.
6.2 Tuition tip
Look for centres that demo the current-balance experiment live—students internalise \(B\)-calculations better when they see the metre reading. Group formats are cost-effective and harness peer reinforcement.
7 Three WA timing rules (reprise)
- 1 mark ≈ 1.5 min — same as SEAB design.
- Copy units before numbers to avoid mis-scaling Tesla ↔ mT.
- Always quote answers to the least precise s.f. among inputs.
8 Further reading
Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.
