Question

Two thin long, parallel wires separated by a distance $d$, carry a current $i$ each in the same direction. They will

• A. Attract each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d^2\right)}$ per unit length.
• B. Repel each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d^2\right)}$ per unit length.
• C. Attract each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d\right)}$ per unit length.
• D. Repel each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d\right)}$ per unit length.

Answer 1

The correct option is C

Attract each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d\right)}$ per unit length.

Step 1: Draw two parallel wires carrying current as follows:

Since the currents flowing in the wires are in the same direction, the wires will attract each other.

Step 2: Equation for force per unit length

The equation for the force per unit length can be written as follows:

$F=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$

Where, $F$ is the force, ${\mu }_0$ is the constant, $i_1$ and $i_2$ are the currents flowing in the wires, and $d$ is the distance between the wires.

Since the current in both the wires is the same $\left(i\right)$, the equation for the attraction force can be written as follows:

$F=\frac{{\mu }_0{i}^2}{2\pi d}$

Hence, the wires attract each other with a force of $\frac{{\mu }_0{i}^2}{\left(2\pi d\right)}$ per unit length.

Therefore, option (C) is correct.