Question

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

• A. repel each other with a force per unit length of $\frac{{\mu }_0{i}^2}{2\pi d}$
• B. attract each other with a force per unit length of $\frac{{\mu }_0{i}^2}{2\pi d}$
• C. repel each other with a force per unit length of $\frac{{\mu }_0{i}^2}{2\pi d^2}$
• D. attract each other with a force per unit length of $\frac{{\mu }_0{i}^2}{2\pi d^2}$

Answer 1

Answer: (B)

attract each other with a force per unit length of $\frac{{\mu }_0{i}^2}{2\pi d}$

The force per unit length between two long current carrying carrying conductors is $F=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$
where d is the distance between the conductors and $i_1$ and $i_2$ are the currents carried by the conductors.
The conductors attract each other if $i_1$ and $i_2$ are in the same direction. Magnetic field created by conductor 1 at the location of the conductor 2 and conductor 2 gets attracted towards conductor 1.
Since $i_1=i_2=i$
$\therefore F=\frac{{\mu }_0{i}^2}{2\pi d}$