# Magnetic fields

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u23-overview/
> Weight: n/a

This unit introduces core magnetic field concepts, interactions with moving charges and currents, and key applications including the Hall effect, forming a foundation for electromagnetism.

**Prerequisites:** Vector mechanics, electric field concepts

## Learning objectives

- Describe magnetic fields and represent them diagrammatically according to CIE syllabus conventions
- Calculate magnetic force on current-carrying conductors and moving charged particles
- Analyze circular and helical motion of charged particles in uniform magnetic fields
- Explain the Hall effect and solve problems involving Hall voltage calculations

## 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](https://www.owlsprep.com/study/cie-9702-u23-magnetic-field-concepts/) — Learn the definition of magnetic flux density, how to draw magnetic field lines for common configurations, and unit conventions.
- [Force on current-carrying conductor](https://www.owlsprep.com/study/cie-9702-u23-force-on-current-carrying-conductor/) — Derive and apply $F = BIL\sin\theta$ for force on a current-carrying wire in a uniform magnetic field.
- [Force on moving charged particle](https://www.owlsprep.com/study/cie-9702-u23-force-on-moving-charged-particle/) — Extend force on current to derive the Lorentz force $F = Bqv\sin\theta$ for a single moving charged particle.
- [Charged particle motion in B-fields](https://www.owlsprep.com/study/cie-9702-u23-charged-particle-motion-in-b/) — Analyze circular and helical motion of charged particles in uniform magnetic fields, and calculate orbital parameters.
- [Hall effect](https://www.owlsprep.com/study/cie-9702-u23-hall-effect/) — Explain the origin of the Hall effect and derive and use the formula for Hall voltage.

## Common pitfalls

- **Wrong:** Forgetting to account for the angle between current/velocity and the magnetic field
  - Why it fails: Force is zero when current/velocity is parallel to the B-field, so $\sin\theta = 0$
  - Correct: Always check the angle between the two vectors before calculating force
- **Wrong:** Using the same force direction for positive and negative moving charges
  - Why it fails: Fleming's left-hand rule is defined for positive conventional current
  - Correct: Reverse the calculated force direction for negative charges such as electrons
- **Wrong:** Assuming all charged particle motion in B-fields is circular
  - Why it fails: Only the perpendicular component of velocity produces centripetal force
  - Correct: Resolve velocity into parallel and perpendicular components to find the full helical path

## Cheatsheet

| Concept | Formula / Definition |
| --- | --- |
| Force on current-carrying wire | $F = BIL\sin\theta$ |
| Lorentz force on moving charge | $F = Bqv\sin\theta$ |
| 1 tesla (unit of B) | $1\ T = 1\ N A^{-1} m^{-1}$ |
| Radius of circular particle path | $r = \frac{mv}{Bq} = \frac{p}{Bq}$ |
| Cyclotron frequency | $f = \frac{Bq}{2\pi m}$ |
| Hall voltage | $V_H = \frac{BI}{nqt}$ |

## 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.

- [Magnetic field concepts (first topic of this unit)](https://www.owlsprep.com/study/cie-9702-u23-magnetic-field-concepts/)
- [Force on current-carrying conductor](https://www.owlsprep.com/study/cie-9702-u23-force-on-current-carrying-conductor/)
- [Force on moving charged particle](https://www.owlsprep.com/study/cie-9702-u23-force-on-moving-charged-particle/)

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