The Force of Charges and Fields
Electromagnetism governs the forces between charged particles and underlies electricity, magnetism, and light. It rests on electric charge, which comes in two signs: like charges repel, opposite charges attract, with charge conserved and quantized.
The force between two point charges is Coulomb's law: proportional to the product of the charges and inversely proportional to the square of the distance — so doubling the separation quarters the force. Rather than picture action at a distance, physics uses the electric field : a charge creates a field in the surrounding space, and another charge feels a force . The field is a quantity defined at every point — one of physics' most powerful abstractions.
Electricity and magnetism, once thought separate, are two aspects of one electromagnetic force:
- Moving charges create magnetic fields (a current in a wire produces a circling field).
- Magnetic fields exert forces on moving charges (the basis of motors).
- A changing magnetic field induces a voltage (Faraday's law) — the basis of generators. Crucially, only a changing field induces; a steady field induces nothing.
Maxwell's equations unified all of this into four laws and revealed something profound: oscillating electric and magnetic fields sustain each other and propagate as electromagnetic waves traveling at the speed of light. Light itself is an electromagnetic wave — as are radio, microwaves, and X-rays, differing only in frequency. This unification, connecting electricity, magnetism, and optics, is one of the crowning achievements of physics, and it rests on the vector calculus and wave mathematics of earlier units.
Common pitfall: getting the sign of the Coulomb force wrong (like charges repel, opposites attract), and thinking a steady magnetic field induces a current. The force falls off as , so doubling the distance quarters it — and two like charges push apart. For induction, Faraday's law depends on the rate of change of the magnetic field: a motionless magnet near a coil induces nothing; current appears only while the field is changing.