Force Between Two Wires (Magnetism)

[medgirl]

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!

 

[Born2bwire]

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.

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.

 

[nlightner]

I can provide a response to this content by breaking down the problem and explaining the steps to solve it. First, let's define some variables to make the problem easier to understand:

I1 = current in the first wire (25 A)
I2 = current in the second wire (25 A)
d1 = distance from first wire to point P (12 cm)
d2 = distance from second wire to point P (5 cm)
d = distance between the two wires (13 cm)
B1 = magnetic field at point P due to the first wire
B2 = magnetic field at point P due to the second wire
B = total magnetic field at point P

Now, using the equation B= [uI]/[2pi (d)], we can calculate the magnetic field at point P due to each wire separately. For the first wire, B1 = [uI1]/[2pi (d1)] = (4pi x 10^-7 Tm/A)(25 A)/[2pi (0.12 m)] = 0.0105 T. Similarly, for the second wire, B2 = [uI2]/[2pi (d2)] = (4pi x 10^-7 Tm/A)(25 A)/[2pi (0.05 m)] = 0.0314 T.

Now, to find the total magnetic field at point P, we can use the principle of superposition. This means that we can simply add the magnetic fields due to each wire together to get the total magnetic field. So, B = B1 + B2 = 0.0105 T + 0.0314 T = 0.0419 T.

In conclusion, the total magnetic field at point P, which is 12 cm from one wire and 5 cm from the other, is 0.0419 T. It is important to note that this is a vector quantity and its direction can be determined using the right hand rule. I hope this explanation helps and good luck on your exam!