Question

A straight wire carrying a current $i_1$ runs along the axis of a circular current $i_2$. Then the force of interaction between the two current carrying conductors is

• A. $\infty$
• B. Zero
• C. $\frac{{\mu }_0}{4\pi }\frac{2i_1{i}_2}{r}$
• D. $\frac{2i_1{i}_2}{r}\frac{N}{m}$

Answer 1

The correct option is B Zero

Direction of magnetic field due to circular current will be perpendicular to the plane of circle i.e. along the axis as shown in the diagram below.
Force due to magnetic field is given as
$d\overrightarrow{F}=I(\overrightarrow{dl}\times \overrightarrow{B})$
Since both vector $\overrightarrow{dl}$ and $\overrightarrow{B}$ are in same direction, the force of intercation between both the wires will be zero.