Electromagnetism and optics

Coulomb’s law has the same shape as Newton’s gravitation, with charges in place of masses and a constant k = 1/(4πε₀) about 8.99 × 10⁹ N·m²/C². Like charges repel. The electric field is the force per unit charge, so the field of a point charge is kq/r². Electric potential is potential energy per unit charge; for a point charge it is kq/r, and the field points from high potential toward low potential for a positive test charge. Voltage, in circuit language, is a potential difference.

Ohm’s law V = IR is a material relation, true for ohmic resistors, not a law on the level of Coulomb. Power dissipated in a resistor is IV, which is also I²R and V²/R. In series, resistances add and the current is common. In parallel, the currents add and the voltage is common, so the reciprocals of resistance add. Kirchhoff’s loop rule is the statement that electrostatic potential is single-valued: the sum of voltage changes around a closed loop is zero.

A charge q moving at velocity v in a magnetic field B feels F = q v × B, magnitude qvB sin θ, direction given by the right-hand rule, and zero when v is parallel to B. Magnetic forces do no work, because they are always perpendicular to the velocity; they change direction, not speed. Changing magnetic flux induces an emf equal to minus the rate of change of flux, which is Faraday’s law, and the minus sign is Lenz’s law: the induced current opposes the change. Maxwell’s correction to Ampère’s law makes the whole set predict electromagnetic waves that travel at c = 1/√(μ₀ε₀).