Electrodynamics/Lorentz Force

We must at this point ask, if a charge is inserted into a system with E and B fields, what will be the effect of those two fields on the charge? In other words, what is the force exerted on a point charge by a combined electromagnetic field?

Force from E Field

${𝐅}_E=q𝐄$

Force from B Field

${𝐅}_B=q𝐯\times 𝐁$

Notice also that in place of a charge q with a velocity, we can use an electric current. This means that a magnetic field will exert a force against a wire carrying a current as such:

${𝐅}_B=I\times 𝐁$

We will touch on the interaction between currents and magnetic fields again later when we discuss Faraday's Law.

Lorentz Force

$𝐅=q𝐄+q𝐯\times 𝐁$