Solve for Magnetic Force with Unequal Length Wires | Quick Question

[Fusilli_Jerry89]

Homework Statement

Quick Question, you know that if two wires are 1 metre apart, both are 10 m long, they both carry 1 A, and the magnetic field they are in is 5 T, you would do the following to solve for force:

F=(4pi x10^-7)(1A)(1A)(10m)/2pi*1
But what if the two wires are different lengths? If one was 10m long, and one was 9m long, would you use the 9m in place of L?

Homework Equations

B=(4 pi x10^-7)I/2*pi*r
F=BIL

The Attempt at a Solution

 

[lippyka]

Yes, you would use the 9m in place of L. The force is equal to the product of magnetic field and current times the length of the wire, so if one wire is longer than the other, you need to use that wire's length in your equation.

 

[m2003]

Yes, you would use the 9m in place of L because the length of the wire affects the strength of the magnetic field it creates. The longer wire would have a slightly stronger magnetic field, so the force between the two wires would be slightly different compared to if they were both 10m long. Therefore, to accurately calculate the magnetic force between the two wires, the length of each wire must be taken into account.