Considering the highly positive feedback on my previous post (100% like ratio), I've decided to make a follow-up! ...or is it a follow-down, since this chapter precedes the previous one?
In 1820, Hans Christian Ørsted made a significant breakthrough in science. When he placed a compass near an electrical wire, the compass didn't point to north. It was then he discovered that there were magnetic fields around an electric current.
Soon after his discovery, Jean-Baptiste Biot and Félix Savart discovered an equation to calculate this magnetic fields. (The Biot–Savart law involves integrals and complicated notations, so I'm not writing it down here.)
In the late 19th century, Hendrik Lorentz derived an equation to calculate a force—which was aptly named Lorentz force—that acts on electric particles moving in a magnetic field. This force is perpendicular to the magnetic field and perpendicular to the object's velocity. The Lorentz force is calculated by adding up the external electric force (qE) with the magnetic force (qv × B). On an ideal particle, one that doesn't have its own electric and magnetic fields, the Lorentz force equation is given by the formula:
F = q(E + v × B)
The Lorentz force also works on an electrical wire carrying electricity in a magnetic field and two parallel electrical wires carrying electricity. Although, you don't see it in everyday life because the force is really, really small.