# Force between Parallel Current Carrying Wires

mitchy16

## Homework Statement

Two parallel wires have currents that have the same direction, but differing magnitude. The current in wire A is I, and the current in wire B is 2I. Which one of the following statements concerning the situation is true?
A) Both wires attract each other with the same force
B) Wire A attracts wire B with twice the force that wire B attracts wire A.
C) Wire A attracts wire B with half the force that wire B attracts wire A.
D) Wire A repels wire B with half the force that wire B attracts wire A.
E) Wire A repels wire B with twice the force that wire B attracts wire A.

F = L I X B

## The Attempt at a Solution

Okay, so I know that wires in the same direction will attract, so that removes options D and E. What I am unsure of though, is why the correct answer is A. While I was working this problem out, I assumed the force would be half that of wire B, due to the formula posted above. Why would the force be the same?
Any and all guidance is appreciated, thank you!

Homework Helper
Gold Member
Why would the force be the same?
Have you heard of Newton's Third Law? If not calculate the force on each wire and be sure to put in the proper expression for B.

• mitchy16
mitchy16
Have you heard of Newton's Third Law? If not calculate the force on each wire and be sure to put in the proper expression for B.
Yes, I had tried relating to Newton's Third Law, and that part makes sense, but if I were to solve for force, would it not be:

Wire A:
F = (L)(2I) X (B)
1/2F = (L)(I) X (B)
Wire B:
F = (L)(I) X (B)

I think I'm just missing something obvious, but I'm not sure what. Thanks!

Homework Helper
Gold Member
What's B for a long wire? Put that in the expression. Of course for wire A you have to put in the B field due to wire B and vice versa for wire B.

On edit: It's a good idea to use subscripts "A" and "B" to distinguish currents and fields.

• mitchy16
Let'sthink
Wire A:
F = (L)(2I) X (B)
1/2F = (L)(I) X (B)
Wire B:
F = (L)(I) X (B)
The "bug" lies here. You need to find the force produced on wire A, (carrying current 2I), due to the field produced by by wire B(carrying current I) and vice a versa. The expressions you have used tells me, as well as it should tell you, that you have used the same B for both!?

• mitchy16
mitchy16
The "bug" lies here. You need to find the force produced on wire A, (carrying current 2I), due to the field produced by by wire B(carrying current I) and vice a versa. The expressions you have used tells me, as well as it should tell you, that you have used the same B for both!?
OH, I understand my mistake now! Thank you so much, that clears it up.