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We know that Electric field or electric force acts on charges at rest and magnetic force acts on charges in motion. But when we combine these two we get what we call as Lorentz force. So I want to know that how can these two forces act on the same charge. Either it should be that E.F acts on the charge (if at rest) or M.F (if in motion). So why do we combine these two in lorentz force. What's the need?

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    $\begingroup$ electric force acts on particle in motion too. $\endgroup$
    – Danny LeBeau
    Commented Jul 16, 2020 at 14:23
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    $\begingroup$ If both electric field and magnetic field are present in the same space, the force on the charge due to electric field is qE , whereas the force due to magnetic field on a charge depends on its velocity, more correctly the force on an electric charge moving with a certain velocity 'V' is given by qVB, if V and B are perpendicular. $\endgroup$
    – user243016
    Commented Jul 16, 2020 at 14:25

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There should be no "should" in

Either it should be that E.F acts on the charge (if at rest) or M.F (if in motion).

Namely as mentioned in the comments, any particle which is electrically charged feels a force due to an electric field $\vec{E}$, equal to $$\vec{F} = q \vec{E}$$

whether it is moving or not. At the same time a charged particle which is moving through a magnetic field $\vec{B}$ feels a force $$\vec{F} = q \vec{v}\times \vec{B},$$ this is an observed fact, as well as the fact that if the particle is charged but not moving, it doesn't feel the magnetic field.

Now, we know by Newton's laws that forces superpose, that is the total force is the addition of forces. The addition of the two above is nothing but the Lorentz force.

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  • $\begingroup$ Thank you so much I had so misunderstandings about it. Now its clear $\endgroup$
    – Vaibhav Raj
    Commented Jul 16, 2020 at 14:32
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Lorentz Force is given as: $$\vec{F}=q\vec{E}+q\vec{v}×\vec{B}$$

The magnetic force will only act on the charge when $\vec{v} \neq 0$ and the angle between velocity and Magnetic field is not the integral multiple of $\pi$.

While Electric field will always act on the charge irrespective of its state of motion.

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