How Do Parallel Current-Carrying Wires Affect Each Other?

[steve12]

Homework Statement

hi,im a bit confused by the following question.i think i have a fairly good idea of most of the solution but the actual wording of the question is stil throwing me.

Q: 3 parallel wires,arranged in the form of an equilateral triangle,of side length 10cm,each carry a current of 50 A in the same direction.Calculate the force on anyone wire due to the other two.

Homework Equations

I used the equation F= 2*10^-7(I1)(I2)/d
a
and arranged wires as follows: *


b* c*

with wires going into page.

The Attempt at a Solution

i calculated the force on the top wire,a, due to b and c:
F=2*10^-7(50)(50)/0.1 = 5.0*10^-3 N in each case,along the line joining a to b and a to c

so this force F is attractive as the currents are in the same direction,yes?
what i am wondering is if i have to calculate the resultant force on a,that is,use for eg the parallelogram rule to find the resultant force, which would point in the direction straight down,or can i simply leave the ans. as is??

is there some sort of convention for expressing this direction or can i just say in the direction indicated on a diagram?

i used the cosine rule and found that the resultant force is (3^1/2)(5*10^-3)N in the direction pointing straight down so that the vector would bisect bc as shown in diagram,does this make sense?
thanks steve

 

[steve12]

ok that didnt work out,wires are meant to look like this:

...a*


b* .... c*



ignore dots

 

[m2003]

Hi Steve,

It seems like you have a good understanding of the problem and have used the correct equation to calculate the force on wire a due to wires b and c. You are correct in saying that the force is attractive since the currents are in the same direction.

As for the direction of the resultant force, you can express it either as the direction indicated on the diagram or as the direction pointing straight down. Both are acceptable ways of expressing the direction.

Using the cosine rule to find the resultant force and its direction makes sense. It is important to consider the direction of the resultant force in this problem since the wires are arranged in an equilateral triangle.

Overall, your solution seems to be correct and you have a good understanding of the problem. Keep up the good work!