Module 3 : Electromagnetism
Lecture 13 : Electric Current and Current Density
  The Lorentz Force
 

We know that an electric field $\vec E$exerts a force $q\vec E$on a charge $q$. In the presence of a magnetic field $\vec B$, a charge $q$experiences an additional force \begin{displaymath}\vec F_m = q\vec v\times\vec B\end{displaymath}

where $\vec v$is the velocity of the charge. Note that

  • There is no force on a charge at rest.
  • A force is exerted on the charge only if there is a component of the magnetic field perpendicular to the direction of the velocity, i.e. the component of the magnetic field parallel to $\vec v$does not contribute to $\vec F_m$.

•  $\vec v\cdot\vec F_m = 0$, which shows that the magnetic force does not do any work.

In the case where both $\vec E$and $\vec B$are present, the force on the charge $q$is given by

\begin{displaymath}\vec F = q(\vec E + \vec v\times\vec B)\end{displaymath}

This is called Lorentz force after H.E. Lorentz who postulated the relationship. It may be noted that the force expression is valid even when $\vec E$and $\vec B$are time dependent

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