Lorentz Force Full

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Lorentz force vector expression?

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1. **Definition**: The Lorentz force is the total electromagnetic force exerted on a point charge by electric and magnetic fields.
2. **Electric Component**: $\vec{F}_e = q \vec{E}$, which acts in the direction of the field for a positive charge.
3. **Magnetic Component**: $\vec{F}_m = q (\vec{v} 	imes \vec{B})$, which acts perpendicular to both velocity and the field.
4. **Unified Expression**: $\vec{F}_{total} = \vec{F}_e + \vec{F}_m = q\vec{E} + q(\vec{v} 	imes \vec{B})$.
5. **Factor out $q$**: **$\vec{F} = q(\vec{E} + \vec{v} 	imes \vec{B})$**.

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