# Chapter 28: Ampere's Law

In the previous chapter, we mapped magnetic fields and explored the force of magnetic fields on moving charges and currents. In this chapter, we will focus on the cause of magnetic fields (moving charges) and how to calculate fields created by current carrying wires. We will use Ampere's law to calculate the magnetic field and use right-hand rules to predict the direction of the magnetic field from an assembly of current carrying wires. As with Gauss's law, to use Ampere's law we depend on the symmetry of the configuration to make the needed simplifications to the calculations. Once we have expressions for fields from current carrying wires, we can investigate interactions between wires. Since a current carrying wire creates a magnetic field, it can exert a force (Lorentz force: **F **= q** v **x** B **= I** L **x** B**) on the current carriers in a nearby wire.

# Table of Contents

## Illustrations

- Illustration 28.1: Fields from Wires and Loops.
- Illustration 28.2: Forces Between Wires.
- Illustration 28.3: Ampere's law and Symmetry.
- Illustration 28.4: Path Integral.

## Explorations

- Exploration 28.1: A Long Wire with Uniform Current.
- Exploration 28.2: A Plate of Current.
- Exploration 28.3: Wire Configurations for a Net Force of Zero.

## Problems

- Problem 28.1: Force between wires.
- Problem 28.2: Adding magnetic fields from wires.
- Problem 28.3: Find unknown currents for a given path integral.
- Problem 28.4: Amperian loop and path integral for uniform field.
- Problem 28.5: Coaxial cable.
- Problem 28.6: Force between wire and cylinder.
- Problem 28.7: Wire with uniform current.
- Problem 28.8: Current carrying plate.
- Problem 28.9: Slinky Solenoid.
- Problem 28.10: Magnetic field of a loop.