# 22: Source of Magnetic Field

- Page ID
- 19532

Learning Objectives

- Understand how to apply the Biot-Savart Law to determine the magnetic field from an electric current.
- Understand how to apply Amp`ere’s Law.
- Understand how to model the forces that are exerted on each other by two wires carrying current.
- Understand how to model a solenoid and a toroid.

In this chapter, we develop the tools to model the magnetic field that is produced by an electric current. We will introduce the Biot-Savart Law, which is analoguous to Coulomb’s Law in that it can be used to calculate the magnetic field produced by any current. We will also introduce Amp`ere’s Law, which can be thought of as the analogue to Gauss’ Law, allowing us to easily determine the magnetic field when there is a high degree of symmetry.

prelude

How does an electromagnet work?

- Current is passed through a magnet, increasing its strength.
- Current is passed through a circular coil, creating a magnetic field.

- 22.1: The Biot-Savart Law
- The Biot-Savart law allows us to determine the magnetic field at some position in space that is due to an electric current. More precisely, the Biot-Savart law allows us to calculate the infinitesimal magnetic field, dB, that is produced by a small section of wire, dl , carrying current, I , such that dl is co-linear with the wire and points in the direction of the electric current.

- 22.3: Ampere’s Law
- Ampere’s Law is similar to Gauss’ Law, as it allows us to (analytically) determine the magnetic field that is produced by an electric current in configurations that have a high degree of symmetry

- 22.4: Solenoids and Toroids
- To create strong magnetic fields, the most practical method is to combine many loops of current together into a “solenoid” (a coil). Electromagnets function on this principle and are ubiquitous in our lives.