Incomplete Cancellation of Magnetic Field

[Angie K.]

Homework Statement

A long pair of wires serves to conduct I = 25.2 A of dc current to and from an instrument. If the wires are of negligible diameter but are d = 2.92 mm apart,

what is the magnitude |B| of the magnetic field a distance L = 9.5 cm from their midpoint, in their plane?

What is the ratio |B|/|BEarth|, where |BEarth| = 5.0 × 10-5 is the magnetic field of the Earth.

Homework Equations

B = mu0*I/2pi*r

The Attempt at a Solution

[/B]
I know that to find B it's just a matter of plugging in the current into the equation above and the r I am not sure about. Someone please clarify this for me?

 

[TSny]

When using the formula for the magnetic field of a long straight wire, remember that r is the distance from the central axis of the wire to the point where you want to find B.

In your case, for one of the wires r will be a little bit less than L. How much less?
For the other wire r will be a little bit more than L. How much more?

 

[Angie K.]

When using the formula for the magnetic field of a long straight wire, remember that r is the distance from the central axis of the wire to the point where you want to find B.

In your case, for one of the wires r will be a little bit less than L. How much less?
For the other wire r will be a little bit more than L. How much more?

Would L be L+r and L-r? Where r is .095m ?

 

[TSny]

Would L be L+r and L-r? Where r is .095m ?

No, L = .095 m.

Note that r is the symbol for the distance from the center of a wire to the the point where you want to find B. For example, consider the wire that is closest to the point where you want to find B. You can see that r for this wire will be a little less than L.

So, if you let x be how much less, then r = L - x. From the diagram and the information given in the problem, can you see how to determine x?

 

[Angie K.]

No, L = .095 m.

Note that r is the symbol for the distance from the center of a wire to the the point where you want to find B. For example, consider the wire that is closest to the point where you want to find B. You can see that r for this wire will be a little less than L. So, if you let x be how much less, then r = L - x. From the diagram and the information given in the problem, can you see how to determine x?

Would the x be half the diameter of the wire?

 

[TSny]

Would the x be half the diameter of the wire?

Yes. Good.

 

[Angie K.]

Yes. Good.

So I have B when r is a little less than L and when it is a little more than L. Now do I just add the two magnetic fields?

 

[TSny]

Yes, but you need to add them as vectors. In other words, you need to take into account the direction of each B field.

 

[Angie K.]

Got it. Thank you very much