# Force Between Two Wires (Magnetism)

## Homework Statement

Two long thin parallel wires 13.0 cm apart carry 25 A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other.

(Sorry I don't have a diagram, but this is essentially a triangle, with sides of 13 cm, 12 cm, and 5 cm, and the point P is at the vertex of the 5 cm and 12 cm sides.

## Homework Equations

B= [uI]/[2pi (d)]

## The Attempt at a Solution

Ok I see that the triangle is a 5-12-13 triangle and thus the Pythagorean theorem applies. I am not sure how this impacts the solution. I obviously need to calculate B for each wire to point P, but once I obtain these values I do not now how to proceed to combine them together to find the total field at P. Simply adding them does not seem correct.

I would really appreciate some guidance. This is not homework, I am reviewing for an exam (tomorrow!) and am really stuck... Thanks!

You need to use vectors for this. The magnetic flux density from a current carrying wire is in the $$\hat{\phi}$$ direction. Calculate the vector in cartesian coordinates (convert from cylindrical) at the desired point for each of the wires and then add the vectors together. The field vector will be of the form $$B\hat{\phi} = B(\alpha_x\hat{x}+\alpha_y\hat{y})$$ where the magnitude of the vector $$\alpha_x\hat{x}+\alpha_y\hat{y}$$ is one.