Electromagnetism

The Force of Charges and Fields

Electromagnetism governs forces between charged particles, uniting electricity, magnetism, and light. It rests on electric charge, where like charges repel and opposite charges attract while charge remains conserved and quantized.

The force between two point charges is Coulomb's law:

$$F = k \frac{q_1 q_2}{r^2}$$

Here, $F$ is force, $k$ is Coulomb's constant, $q_1$ and $q_2$ are charges, and $r$ is distance. Because the force is inversely proportional to $r^2$, doubling the separation quarters the force.

Instead of action at a distance, physics uses the electric field ($\vec{E}$). A charge creates this field in surrounding space, and a test charge feels a force given by $\vec{F} = q\vec{E}$.

Unifying Fields and Waves

Electricity and magnetism are two aspects of one electromagnetic force, linked through induction and moving charges:

Maxwell's equations unified these laws, revealing that oscillating fields propagate as electromagnetic waves at the speed of light. Light itself is an electromagnetic wave.

Common pitfall: A steady magnetic field induces nothing. Faraday's law requires a rate of change; a motionless magnet near a coil creates zero current.