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. $\frac{{\mu }_0\text{iqv}}{2\pi \text{a}}$
• B. $\frac{{\mu }_0\text{qv}}{3\pi a^2}$
• C. $\frac{{\mu }_0{\text{q}}^2\text{v}}{2\pi a^2}$
• D. $\frac{{\mu }_0\text{ivq}}{\text{3}\pi a}$

Answer 1

Answer: (A)

$\text{F}=\text{I}\ell \text{B}=\lambda \text{vLB}$
$\text{F}=\text{q}\text{vB}$
$\text{F}=\text{qv}\frac{{\mu }_0}{4\pi }\frac{2\text{i}}{\text{a}}=\frac{{\mu }_0\text{iqv}}{2\pi \text{a}}$