Unit Overview

Magnetic fields

CIE A-Level Physics· 5 min read 📊 n/a

1. Unit at a glance

This unit builds incrementally from fundamental definitions to practical applications, connecting electricity, magnetism and Newtonian mechanics. We start with describing magnetic fields, then move to calculating forces on currents and individual charges, analyze charged particle motion, and end with the Hall effect, a widely used technique for measuring magnetic flux density. This unit is essential prerequisite knowledge for electromagnetic induction, the next core topic in electromagnetism.

Below is the full list of sub-topics in this unit:

Magnetic field concepts

Learn the definition of magnetic flux density, how to draw magnetic field lines for common configurations, and unit conventions.

★⏱ 6 min

Force on current-carrying conductor

Derive and apply $F = B I L sin θ$ for force on a current-carrying wire in a uniform magnetic field.

★★⏱ 7 min

Force on moving charged particle

Extend force on current to derive the Lorentz force $F = B q v sin θ$ for a single moving charged particle.

★★⏱ 6 min

Charged particle motion in B-fields

Analyze circular and helical motion of charged particles in uniform magnetic fields, and calculate orbital parameters.

★★★⏱ 10 min

Hall effect

Explain the origin of the Hall effect and derive and use the formula for Hall voltage.

★★★★⏱ 8 min

2. Common Pitfalls

Wrong move:

Forgetting to account for the angle between current/velocity and the magnetic field

Why:

Force is zero when current/velocity is parallel to the B-field, so $sin θ = 0$

Correct move:

Always check the angle between the two vectors before calculating force

Wrong move:

Using the same force direction for positive and negative moving charges

Why:

Fleming's left-hand rule is defined for positive conventional current

Correct move:

Reverse the calculated force direction for negative charges such as electrons

Wrong move:

Assuming all charged particle motion in B-fields is circular

Why:

Only the perpendicular component of velocity produces centripetal force

Correct move:

Resolve velocity into parallel and perpendicular components to find the full helical path

3. Quick Reference Cheatsheet

Concept	Formula / Definition
Force on current-carrying wire	$F = B I L sin θ$
Lorentz force on moving charge	$F = B q v sin θ$
1 tesla (unit of B)	$1 T = 1 N A^{- 1} m^{- 1}$
Radius of circular particle path	$r = \frac{m v}{B q} = \frac{p}{B q}$
Cyclotron frequency	$f = \frac{B q}{2 π m}$
Hall voltage	$V_{H} = \frac{B I}{n q t}$

What's Next

Begin your study of this unit with the first sub-topic below to build your foundational understanding of magnetic fields. Once you complete all sub-topics in this unit, you can progress to the first sub-topic of the next unit on electromagnetic induction, which extends the magnetic field concepts you will learn here.