Question

Electric charge $q$ is uniformly distributed over a rod of length $l$ . The rod is placed parallel to a long wire carrying a current $i$ . The separation between the rod and the wire is $a$ . Find the force needed to move the rod along its length with a uniform velocity $v$ .

• A. $\frac{\mu _{0} \textit{iqv}}{2 \pi \textit{a}}$
• B. $\frac{\mu _{0} \textit{qv}}{3 \pi a^{2}}$
• C. $\frac{\mu _{0} \textit{q}^{2} \textit{v}}{2 \pi a^{2}}$
• D. $\frac{\mu _{0} \textit{ivq}}{\text{3} \pi a}$

Answer 1

Answer: (A)

$\text{F} = \text{I} \ell \text{B} = \lambda \text{vLB}$
$\text{F} = \text{q} \text{vB}$
$\text{F} = \text{qv} \frac{\mu _{0}}{4 \pi } \frac{2 \text{i}}{\text{a}} = \frac{\mu _{0} \text{iqv}}{2 \pi \text{a}}$