Question

A current-carrying wire of area $A$, length $l$, number of density of charge carriers $n$ is placed in a region of external magnetic field $B$. What will be net force on charged carriers?

• A. $(n A l) q\left( v _{d} \times B \right)$
• B. $q\left( v _{d} \times B \right)$
• C. $n q\left( v _{d} \times B \right)$
• D. $A l q\left( v _{d} \times B \right)$

Answer 1

Answer: (A)

The total number of mobile charge carriers in wire will be $n A l$.
For a steady current $I$ in this conducting wire, we may assume that each mobile carrier has an average drift velocity $v _{d}$.
In the presence of an external magnetic field $B$, the force on these carriers is given by
$F =(n A l) q\left( v _{d} \times B \right)$