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According to my text book:

The Lorentz Force F on a charged particle moving in an electromagnetic field is given by:

$$F= qE + q(v\times B)$$

then it states that "it is to be pointed out that only the electric force does work, while no work is done by the magnetic force which is simply a deflecting force."

How can this by true? Won't the the magnetic force have a considerable magnitude? Will it now impart kinetic energy to the charge? Any explanations will help a lot. Please keep the terminology simple, thanks.

Pierre Paquette
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Batwayne
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3 Answers3

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Work is done at a rate of $\vec{F} \cdot \vec{v}$. So any force component perpendicular to the velocity at all times cannot do any work classically. The kinetic energy remains unchanged because for the kinetic energy, only the magnitude of the velocity and not its direction is important. All that magnetic force does is change the direction of the velocity while keeping the velocity magnitude constant and that does not need any work.

Sanya
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While this statement is true, it should be stressed that magnetic force does not do work IN REFERENCE OF THE MAGNETIC FIELD. If viewed in other frame of reference( often when the field is moving relative to you), it may do work.

Sam
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The fact that the magnetic forces do not work is not owing to the smallness or largeness of the magnitude of the magnetic field or magnetic force. But it is owing to the direction of the magnetic force relative to the direction of the velocity of the charged particle.

The magnetic field $\vec{B}$ produces a force $\vec{F}$ on a charged particle of charge $q$ and velocity $v$ according to the formula,

$\vec{F}=q(\vec{v}$x$\vec{B})$

As implied by this formula, this force will always be perpendicular to the velocity of the particle and thus the power imparted to the particle via this force, $\vec{F}.\vec{v}$ $=0$, always. Thus no amount of energy is transferred by the means of magnetic forces to the particle and thus the magnetic forces do not alter the speed of the particles.