Module 3 : MAGNETIC FIELD
Lecture 14 : Force on a Current Carrying Conductor
Force on a Current Carrying Conductor
A conductor has free electrons which can move in the presence of a field. Since a magnetic field exerts a force $q\vec v\times\vec B$on a charge moving with a velocity $\vec v$, it also exerts a force on a conductor carrying a current.
Consider a conducting wire carrying a current $I$. The current density at any point in the wire is given by'
 
\begin{displaymath}\vec J = ne\vec v\end{displaymath}
  where $n$is the number density of electrons having a charge $e$each and $\vec v$is the average drift velocity at that point.
  Consider a section of length $dl$of the wire. If $A$is the cross sectional area of the section oriented perpendicular to the direction of $\vec J$, the force on the electrons in this section is
  \begin{displaymath}d\vec F = dq\vec v\times\vec B\end{displaymath}
  where $dq$is the amount of charge in the section
 
\begin{displaymath}dq = neAdl\end{displaymath}
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