Question

In two current carrying conductors parallel currents ________ , anti parallel currents _________

• A. attract
• B. repel

Answer 1

Step 1: Two Current Carrying Conductors

Let us consider two long parallel wires, ($1$ and $2$) carrying currents $I_1$ and $I_2$, separated by a distance $a$. The conductor $1$ produces a magnetic field

$B_1=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{2I_1}{a}$

At the position of conductor $2$. It is directed perpendicular to the conductor $2$.

The force $d\overrightarrow{F}$ acting on the element $d\overrightarrow{l_2}$ of the conductor $2$ due to $\overrightarrow{B_1}$ is

$d\overrightarrow{F}=I_2\left(d\overrightarrow{l_2}\times \overrightarrow{B_1}\right)$

$\Rightarrow \left|d\overrightarrow{F}\right|=dF=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{2I_1{I}_2}{a}d{l}_2$

Step 2: Nature of attraction

This force is directed towards the conductor $1$, i.e., attractive if $I_1$ and $I_2$ flow in the same direction.

On the other hand, the force is directed away from the conductor $1$ if $I_1$ and $I_2$ flow in opposite directions.

The type of force is dependent on the magnetic flux around the two conductors.

The force per unit length of each wire is of magnitude

$\left|\overrightarrow{F}\right|=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{2I_1{I}_2}{a}$

And directed perpendicular to their lengths.

Hence, in two current-carrying conductors parallel currents attract, and anti-parallel currents repel.