Magnetic Fields

Moving charges create magnetic fields. The field’s direction is given by the right-hand rule.

Magnetic Force on a Charge

The force on a charge moving in a magnetic field is

\[ \vec{F} = q \vec{v} \times \vec{B} \] where \( q \) is the charge, \( \vec{v} \) is velocity, and \( \vec{B} \) is magnetic field.

Magnetic Force on a Current

A wire carrying current in a magnetic field experiences a force:

\[ \vec{F} = I \vec{L} \times \vec{B} \]

Calculus Link

Integrals and derivatives help us analyze changing fields and forces, especially in loops and coils.

Real-World Relevance

Magnetic forces run electric motors and help MRI machines create detailed images of our bodies.