# Video: Magnetic Force Between Two Long Straight Wires

Ed Burdette

Two long, straight wires are parallel and 10 cm apart. One carries a current of 2.0 A, the other a current of 5.0 A. What is the magnitude of the force per unit length between the wires?

02:02

### Video Transcript

Two long, straight wires are parallel and 10 centimeters apart. One carries a current of 2.0 amps, the other a current of 5.0 amps. What is the magnitude of the force per unit length between the wires?

We can call the distance separating the wires, 10 centimeters, ๐. And we can call the current in the first wire, 2.0 amps, ๐ผ sub one and the current in the second wire, 5.0 amps, ๐ผ sub two. We want to solve for the force per unit length between the wires. Weโll call that ๐น over ๐ฟ. In a situation with two long, straight wires that are parallel to one another, with the wires both carrying current and separated from one another by a distance ๐, thereโs a mathematical relationship that describes the force, itโs a magnetic force, between these parallel wires.

That magnetic force per unit length, ๐น sub ๐ต divided by ๐ฟ, is equal to the permeability of free space times the product of the two currents all over two ๐ times the distance between the current-carrying wires ๐. ๐ naught, which is a constant, weโll treat as exactly 1.26 times 10 to the negative sixth teslas meters per ampere. So the force between the wires per unit length is equal to ๐ naught times ๐ผ one times ๐ผ two over two ๐ ๐. We know each of these values. And so weโre ready to plug in and solve for ๐น over ๐ฟ.

When we do plug in, weโre careful to use units of meters for our distance ๐. When we enter all these values on our calculator, we find ๐น over ๐ฟ is 2.0 times 10 to the negative fifth newtons per meter. Thatโs the magnitude of the force per unit length between these current-carrying wires.