Force Between Two Wires (Magnetism)

In summary, the problem involves calculating the magnetic field at point P, located 12.0 cm from one wire and 5.0 cm from the other, given two long parallel wires carrying 25 A currents in the same direction and separated by 13.0 cm. The Pythagorean theorem can be used to find the distance between the two wires and the magnetic flux density equation can be used to calculate the field at point P for each wire. These values can then be added using vector addition to find the total magnetic field at point P. Alternatively, trigonometry can be used to determine the direction of the fields from each wire.
  • #1

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!
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  • #2
You need to use vectors for this. The magnetic flux density from a current carrying wire is in the [tex]\hat{\phi}[/tex] 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 [tex]B\hat{\phi} = B(\alpha_x\hat{x}+\alpha_y\hat{y})[/tex] where the magnitude of the vector [tex]\alpha_x\hat{x}+\alpha_y\hat{y}[/tex] is one.

You can also use trigonometry to find out what the direction of the fields are from each wire if you feel more comfortable doing that but it will probably involve more work.

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