Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

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œ‹ times the distance between the current-carrying wires ๐‘‘. ๐œ‡ 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œ‡ naught times ๐ผ one times ๐ผ two over two ๐œ‹ 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.