Consider the long, straight, current-carrying wires shown in the figure. One wir
ID: 2052791 • Letter: C
Question
Consider the long, straight, current-carrying wires shown in the figure. One wire carries a current of 62 A in the positive y direction; the other wire carries a current of 4.5 A in the positive x direction.
a.) At which of the two points, A or B, do you expect the magnitude of the net magnetic field to be greater? Explain.
b.) Calculate the magnitude of the net magnetic field at points A and B.
Explanation / Answer
Part A)
When you apply the right hand rule for current carrying wires, you can determine the magnetic field direction.
At point A, the magentic field produced by the vertical wire will point out of the page. The magnetic field from the horizontal wire will also point out of the page at that point. Therefore both vectors are pointing out of the page and add together to give a stronger field.
At point B, the magentic field produced by the vertical wire will point into of the page. The magnetic field from the horizontal wire will still point out of the page. Therefore the vectors will subtract causing a net smaller field.
The result... Point A will have the stronger field.
Part B)
The magnetic field is found by the formula B = oI/2r
At both points A and B, the magnetic field from the vertical wire is
B = (4 X 10-7)(6.2)/[(2)(.16)]
B = 7.75 X 10-6 T or 7.75T
At both points A and B, the magnetic field from the horizontal wire is
B = (4 X 10-7)(4.5)/[(2)(.16)]
B = 5.63 X 10-6 T or 5.63T
We know that at point A, the two field vectors will add, so...
7.75 X 10-6 T + 5.63 X 10-6 T = 1.34 X 10-5 T or 13.4 T pointing out of the page
We know that at point B, the two field vectors will subtract.
The subtraction will be
7.75 X 10-6 T - 5.63 X 10-6 T = 2.12 X 10-6 T or 2.12 T pointing into the page