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Physics

Magnetic Fields and Magnetic Force

A High School and Early College Physics Primer

Magnetism trips up more physics students than almost any other topic. The forces point in strange directions, the right-hand rule feels arbitrary, and most textbooks bury the core ideas under pages of derivations. If you have an AP Physics exam, a college midterm, or a unit test coming up and you need to get solid on magnetic fields fast, this guide was written for you.

**TLDR: Magnetic Fields and Magnetic Force** covers exactly what the title promises — nothing more, nothing less. In about 15 pages you will learn what a magnetic field is and how to read field-line diagrams, how to apply **F = qv × B** to find the force on a moving charge, why that force curves particles into circles (and how mass spectrometers use that fact), how to calculate the force and torque on current-carrying wires, and where the fields produced by straight wires, loops, and solenoids come from. Electromagnetic induction is left for a separate volume so this one stays focused.

The book is designed for high school students in grades 9–12 and early college students hitting magnetism for the first time or needing a fast review. Every term is defined in plain language, every formula is paired with a worked example, and common mistakes — like confusing the direction of magnetic force on positive versus negative charges — are called out and corrected directly.

If you want a concise high school physics magnetism exam prep resource that gets to the point, pick this up and start page one.

What you'll learn
  • Describe what a magnetic field is, its units, and how to visualize it with field lines
  • Apply the right-hand rule to find the direction of magnetic force on a charge or current
  • Calculate the magnetic force on a moving charge using F = qvB sin(theta) and on a wire using F = BIL sin(theta)
  • Analyze circular motion of charged particles in uniform magnetic fields, including radius and period
  • Compute magnetic fields produced by long straight wires, loops, and solenoids, and the force between two parallel wires
What's inside
  1. 1. What Is a Magnetic Field?
    Introduces magnetic fields as a vector field around magnets and moving charges, with units, field lines, and the link between magnetism and electricity.
  2. 2. The Magnetic Force on a Moving Charge
    Develops F = qv x B, the right-hand rule, and why magnetic force does no work, with worked examples for charges moving through uniform fields.
  3. 3. Charged Particles Moving in Circles
    Shows how a uniform magnetic field bends a charged particle into a circle or helix, and derives the radius, period, and frequency used in mass spectrometers and cyclotrons.
  4. 4. Magnetic Force on Current-Carrying Wires
    Extends the force law to wires using F = IL x B, treats torque on current loops, and explains how electric motors work.
  5. 5. Magnetic Fields Produced by Currents
    Covers fields from a long straight wire, a circular loop, and a solenoid, plus the force between two parallel wires using the Biot-Savart and Ampere ideas qualitatively.
Published by Solid State Press
Magnetic Fields and Magnetic Force cover
TLDR STUDY GUIDES

Magnetic Fields and Magnetic Force

A High School and Early College Physics Primer
Solid State Press

Magnetic Fields and Magnetic Force

A High School and Early College Physics Primer

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're a high school student doing AP Physics magnetism review, a college freshman in an introductory physics course, or a self-studier who needs high school physics magnetism exam prep before a unit test, this book was written for you. It assumes you know basic algebra and have a rough idea what electric charge is — nothing more.

This short physics study guide for beginners covers exactly what the title promises: magnetic fields, the magnetic force on moving charges, charged particle circular motion physics, magnetic fields and current-carrying wires explained, and the fields that currents themselves produce. The right-hand rule, magnetic force practice problems, and the formulas behind each concept are all here. About 15 pages, no filler.

Work through it in order — the sections build on each other. Pause at every worked example and try to solve it before reading the solution. Then use the problem set at the end to find out what you actually know.

Contents

  1. 1 What Is a Magnetic Field?
  2. 2 The Magnetic Force on a Moving Charge
  3. 3 Charged Particles Moving in Circles
  4. 4 Magnetic Force on Current-Carrying Wires
  5. 5 Magnetic Fields Produced by Currents
Chapter 1

What Is a Magnetic Field?

Every magnet, every current-carrying wire, and every moving charged particle is surrounded by a magnetic field — a vector field that fills the space around it and exerts forces on other magnets and moving charges nearby. "Vector field" means that at every point in space the field has both a magnitude (how strong it is) and a direction (which way it points). The symbol for magnetic field is B.

Think of B the way you already think of a gravitational field near Earth: invisible, fills space, and only reveals itself when something responds to it. The difference is that a magnetic field only acts on charges that are moving. A stationary charge sits in a magnetic field without feeling a thing. That quirk drives almost everything that makes magnetism interesting, and you will see its full consequences in the next section.

Units: Tesla and Gauss

Magnetic field strength is measured in teslas (symbol T), the SI unit named after Nikola Tesla. One tesla is a strong field — a powerful hospital MRI machine runs at 1–3 T, and a small refrigerator magnet produces only about 0.005 T. Because everyday magnetic fields are often much smaller than one tesla, physicists and engineers also use the gauss (symbol G), where

$1 \text{ T} = 10{,}000 \text{ G}$

Earth's magnetic field at the surface is roughly 0.5 G, or $5 \times 10^{-5}$ T. Knowing these benchmarks helps you catch errors: if a calculation gives you a field of 500 T for a household wire, something went wrong.

Visualizing the Field: Field Lines

Just as you can draw electric field lines to picture an electric field, you can draw magnetic field lines to picture B. Three rules govern them:

  • Lines point in the direction a compass needle's north pole would point if placed there.
  • Lines form closed loops — they never start or stop mid-space.
  • Where lines are close together, the field is strong; where they are spread apart, it is weak.
Keep reading

You've read the first half of Chapter 1. The complete book covers 5 chapters in roughly fifteen pages — readable in one sitting.

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