Plasma on the surface of the sun traces out the immense magnetic field lines.

The electromagnetic field has two parts, the electric field and the magnetic field (also called the B field). We can begin to understand these fields through their respective forces.



The electric force is an interaction between charged particles.



The magnetic force is an interaction between moving charged particles.

Moving charged particles create a magnetic field. Charges moving through a magnetic field feel a force. Moving through a magnetic field changes the motion of charged particles. The force exerted on a charged particle by a magnetic field is called the Lorentz force.



A magnetic field affects the motion of charged particles, which in turn affects the magnetic field, which affects the motion of the particles, which affects the field, which affects the particles...



A single charged particle is called a monopole and has radial electric field lines, where a pair of oppositely charged particles is a dipole with dipole E field lines.



Magnetic field lines give information about the magnetic field similar to electric field lines. Field lines in both cases are mathematic constructs illustrating the properties of the field. The field is stronger where the lines are closer together, and the lines are labeled with arrows to indicate the direction of the vector field. Note that the direction of the magnetic field of a ferromagnet like this bar magnet point from North to South outside the magnet.

Iron filings around a bar magnet show the magnetic field lines. Compases are just magnets that are free to turn to align with the magnetic field.

Magnetic monopoles do not exist. Every magnetic field has at least a dipole structure.



The magnetic field of two bar magnets is similar to two electric dipoles placed near each other.



Earth's magnetic field arises from the rotation of its molten metal outer core. Although it is actually very complex, we often approximate it as a bar magnet. Note that the north magnetic pole is actually the south pole of the "bar magnet."



The magnetic field of a permanent magnet, like a bar magnet, is caused by magnetic domains in which the spins of electrons are aligned.

The Biot-Savart law

A moving charged particle creates a magnetic field, given by the equation above. This equation is called the Biot Savart law.



The magnetic field has units of teslas, equal to Newtons per Amp-meter. The symbol μ₀ is called the permeability constant.



The Biot-Savart law is a vector equation. We can find the direction of the magnetic field produced by a moving charged particle by using the right-hand rule.

Sample questions

Consider a proton at the origin with constant v_x = 1.0 x 10⁷ m/s. Use q = 1.60 x 10^-19 C.

1. Find the magnitude and direction of the magnetic field caused by the motion of this charged particle at the position (x, y, z) = (0, 1.0 mm, 0).

2. Find the magnitude and direction of the magnetic field caused by the motion of this charged particle at the position (x, y, z) = (1.0 mm, 0, 0).