The figure below shows two current carrying wires and the directions of the currents they carry. The wires carry the following currents: I1 = 7.1 A and I2 = 8.9 A. Wire 1 is at (0, 5.8) mm; wire 2 is at (15.1, 0) mm; point P is at (15.1, 5.8) mm. Wire 1 is pointing into the page, and wire 2 is pointing out of the page.

Question

What are the magnitude and direction (measured with respect to the +x direction) of the total magnetic field due to the two wires at point P?

I used the equation B = (µoI)/(2ðR) to solve for each vector. Wire 1 produces a downward magnetic field on point P, and wire 2 produces a leftward magnetic field on point P. Then, I used the pythagorean theorem to solve for the net magnetic field. I found the net magnetic field to be 3.21E-4 T and the direction to be 17.02 degrees, but this answer is incorrect. What am I doing wrong?

Answer 1

First of all, thank you for showing your work. So few of the students do, despite out pleading. Thank you also for clearly describing the Figure that could not be shown.

It seems you went about the problem in the right way. The fields due to the two different wires at P are perpendicular, so the Pythagorean theorem should give the resultant.

I also abree with your individual B field directions, using the right hand rule.

The equation
B = (µo*I)/(2*pi*R)
is correct for the individual field contributions of each wire. Did you convert the distances R to meters?

Answer 2

I used that equation to solve for the contributions from each wire. I accidently used the equation for magnetic field for a loop (instead of this wire equation) the first time I submitted the homework problem. The angle was incorrect the first time I submitted it too, but it is the same even after I corrected my error. I used the magnetic field components to solve for the angle. I did tan(theta) = B1/B2 to solve for the angle of the net magnetic field above the x axis. I must be doing that part wrong. Thank you very much for your help.