Electrodynamics/Lorentz Force

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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?

[edit] Force from E Field

\mathbf{F}_E = q\mathbf{E}

[edit] Force from B Field

\mathbf{F}_B = q\mathbf{v} \times \mathbf{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:

\mathbf{F}_B = I \times \mathbf{B}

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

[edit] Lorentz Force

\mathbf{F} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}
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