Calculating Magnetic Field of Two Wires at a Point (x, y)

[twalters84]

Homework Statement

One wire, lying on the x-axis, carries a current of 8.0 A in the positive x-direction. Another wire, lying on the y-axis, carries a current of 12 A in the positive y-direction. What is the magnitude of the magnetic field at (x, y) = (8.0 cm, 12.0 cm)?

Homework Equations

B = (uI) / (2*PI*r)

u = 4*PI*10^-7

The Attempt at a Solution

First, I found each magnetic field separately.

B1 = ((4*PI*10^-7)(12)) / (2*PI*(8/100)) = 3*10^-5 T
B2 = ((4*PI*10^-7)(8)) / (2*PI*(12/100)) = 1.3*10^-5 T

This is the point I am stuck. The answer key says the answer is 1.7*10^-5 T. I see that you can get that answer by:

3*10^-5 T - 1.3*10^-5 T = 1.7*10^-5 T

However, I do not understand the reasoning behind this. Could somebody explain this to me? Thanks in advance.


Travis Walters

 

[Shooting Star]

For the Ix, the field at the given pt is toward +ve z, and for Iy, the field is toward -ve z.

Think about how the magnetic field lines are circular about the wire. Here, at the given point, they are in opp directions.

 

[twalters84]

Hey there,

I see what you mean about them being in opposite directions.

However, since B1 is in the negative Z direction, would that answer be -3*10^-5 T instead of 3*10^-5 T? Likewise, since B2 is in the positive Z direction, would that answer be 1.3*10^-5 T instead of -1.3*10^-5 T?

If that is the case adding these two quantities togather would yield -1.7*10^-5 T and not 1.7*10^-5 T correct? Is the magnitude the absolute value or should it be negative?

Thanks once again for any clarification.


Travis Walters

 

[Shooting Star]

The magnitude is simply the absolute value without regard to the sign and so is always +ve.