Question

Four very long straight wires carry equal currents in the $+z$- direction. They intersect the $xy$-plane at $(x,y)=(-a,0),(0,a),(a,0)$ and $(0,-a).$ The magnetic force exerted on the wire at position $(-a,0)$ is along-

• A. $+y$-axis
• B. $-y$-axis
• C. $+x$-axis
• D. $-x$-axis

Answer 1

The correct option is C $+x$-axis


Force per unit length between two parallel infinite current carrying conductors is,

$\frac{dF}{dL}=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$

If they carry current in the same direction, then force between them will be attractive in nature. So, the direction of force experienced by the wire $\text{D}$ is shown below.


As we can see, the angle made by $\overrightarrow{F_{DA}}$ and $\overrightarrow{F_{DC}}$ with $x$- axis is ${45}^{\circ }.$ Thus, vertical component of $\overrightarrow{F_{DA}}$ and $\overrightarrow{F_{DC}}$ cancel each other. Only its horizontal components exists which will be along $x-$axis.

The resultant force on the current carrying conductor $\text{D}$ will be directed along the $+x$-axis and its magnitude is,

$\therefore F_{net}=F_{DB}+\sqrt{{F_{DA}}^2+{F_{DC}}^2}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option $\left(\text{C}\right)$ is the correct answer.

Why this question ? To understand the concept of force between the two straight parallel current carrying conductors.