In the early 19th century, electricity and magnetism were viewed as two separate areas of physics. Through the experimental work of Michael Faraday and the subsequent mathematical synthesis by James Clerk Maxwell, these two fields were unified into the single framework of electromagnetism.

A central discovery of electromagnetism is that moving charges generate their own magnetic fields, causing them to experience a force when traveling through an external magnetic field. This fundamental interaction forms the operating principle behind electric motors.

Conversely, when electric charges experience a changing magnetic field—or a change in magnetic flux—a force is induced, generating an electromotive force (EMF). This principle forms the foundation of electrical power generation.

The following lessons examine the key physical principles and mathematical models that govern these electromagnetic behaviors.

We know that stationary electric charges experience electrostatic forces when placed within an electric field. But what happens when a charged particle is already in motion as it enters a uniform electric field?

When a moving charge enters a uniform electric field perpendicularly, it experiences a constant force directed parallel to the field lines (F = qE). Because this force acts perpendicular to the particle's initial velocity, it produces a constant acceleration in one dimension while the perpendicular velocity remains unchanged. As a result, the charge follows a parabolic trajectory—much like a projectile moving through a gravitational field.

The following video uses the historic example of a Crookes tube (cathode ray tube) to demonstrate how magnetic and electric fields deflect beams of electrons, breaking down the underlying mathematical principles that govern moving charges in electric fields.