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All lessons Electromagnetism24 min

Magnetic Fields and Forces

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On the syllabus: GCSE Physics · A-Level Physics

← Series and Parallel CircuitsElectromagnetic Induction →
01
Hook
02
Explore
03
Formalize
04
Practice
05
Challenge
Interactive simulation
01

Hook

Inside an MRI machine, patients are surrounded by a magnetic field 60,000 times stronger than Earth's — yet they feel nothing, and the machine doesn't push them around. But if a paper clip gets close to that same magnet, it shoots across the room like a bullet. How can a magnetic field be lethal to a paper clip and harmless to a human being at the same time?

02

Explore

Complete previous stage
03

Formalize

Complete previous stage
04

Practice

Complete previous stage
05

Challenge

Complete previous stage

Magnetic Fields and Forces — the short version

The question

Inside an MRI machine, patients are surrounded by a magnetic field 60,000 times stronger than Earth's — yet they feel nothing, and the machine doesn't push them around. But if a paper clip gets close to that same magnet, it shoots across the room like a bullet. How can a magnetic field be lethal to a paper clip and harmless to a human being at the same time?

Electric motors, MRI machines, particle accelerators, and the Earth's own magnetic field all operate on the same principle: moving charges create magnetic fields, and magnetic fields exert forces on moving charges. Mastering these two ideas unlocks the mechanism behind virtually all electrical technology.

The key idea

A long straight wire carrying current I produces a circular magnetic field around it. The field strength B depends on current and distance but not on the charge itself. A charge moving through a magnetic field experiences a force perpendicular to both its velocity and the field — the Lorentz force.

The right-hand rule encodes the direction: for a wire carrying current upward, wrap your right hand around it with the thumb pointing up — your fingers curl in the direction of B (counterclockwise when viewed from above). Magnetic forces never do work on charges because F is always perpendicular to v — they change direction but not speed. This is why a compass needle aligns with Earth's field without energy input. Electromagnets, speakers, and particle accelerators all rely on the Lorentz force F = qv×B.

The formula

B=μ0I2πrF=qvBsin⁡θB=2πrμ0​I​F=qvBsinθ
  • ·B = magnetic field strength (tesla
  • ·T)
  • ·μ₀ = permeability of free space (4π×10⁻⁷ T·m/A)
  • ·I = current (A)
  • ·r = distance from wire (m)
  • ·F = force on a moving charge (N)
  • ·q = charge (C)
  • ·v = speed of charge (m/s)
  • ·θ = angle between v and B

Related lessons

All Electromagnetism lessons
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  • Capacitors24 min
  • Electric Fields22 min
  • Lenz's Law24 min