Determining Distance Between Crossed Wires for Magnetic Field Threshold

[Taryn]

AMPS AND DETERMININ DISTANCE, urgent please help

Crossed wires (a)
Two long current-carrying wires cross at an angle of 37° ("theta" is half of this) as shown in the figure below. The magnitude of the current is the same in each wire, I = 177 A. A wood mouse is running along the dashed line midway between the wires towards the point where the wires cross. The mouse turns back at point P, some distance x from the wire crossing point, because the magnetic field strength reaches an unbearable 8.7 mT. Determine the distance x (in cm).

Okay I am completely stuffed on how to begin this problem, I don't really know where to start... maybe I could be given some help as how to relate distance to the B and I!
okay wats confusin me... is how to find the force in order to find the length... I was thinkin bout usin, F=IlBsin(theta)
But yeah Id really like a hint please!

 

[Hootenanny]

The magnetic field of a current carrying wire is given by;

$$B = \frac{\mu_{0}I}{2\pi r}$$

Where r is radial / perpendicular distance from the wire. I cannot as yet see your attachment, so I am sorry that I can be of no further help at the moment. However, I can say that you will need to think about a vector sum and will probably need to resolve the vectors.

~H

 

[Taryn]

I thought that that would only work for a circle and so mew/2pi is the value 2.7E-7!
Anyway I will give that a go but when you see that attachment then I would love to hear your thoughts thanks!

 

[Taryn]

okay so this is wat I just tried r=(2.7E-7*177)/8.77E3 except this gave me the complete wrong answer... I got 0.000005 or somethin like that and the answer is actually 2.56!

 

[big man]

hey,

I'm not sure if you're in any hurry for this, but if you are then you might want to try hosting the image on http://imageshack.us/
Then just come back here and post the link to the image.

 

[Ouabache]

I thought that that would only work for a circle and so mew/2pi is the value 2.7E-7!

Actually you are talking about a circle. We describe circular paths traced out by the B-field extending radially from a wire carrying current. At a distance r, in the expression that Hoot gave, the magnitude of the B-field, is some fixed value as it crosses the dotted line. It is also the same fixed value at every point in space along the circle traced out along that radius. You've probably convinced yourself (by the right-hand-rule) that the Bfield lines from each wire taken together, are aiding. (if you are not sure what I mean, please ask).

okay so this is wat I just tried r=(2.7E-7*177)/8.77E3 except this gave me the complete wrong answer... I got 0.000005 or somethin like that and the answer is actually 2.56!

You’re on the right track. Be careful what value (and units) you are using for μo. For this question I would choose this constant in T m/A as in this reference. I also recommend leaving it expressed as they give $4 \pi x 10^-7$ and do your fractional simplification later (example: $\pi$’s will cancel). Also for B, by superposition, the sum total of the B-field contributions from each wire is 8.7mT. Since both wires are the same distance from the dotted axis, each wire contributes 1/2 that.

Now what does this answer give you? (the perpendicular length from the wire to the dotted axis). But you’re not asked for that, your looking for x. You’ve got a right triangle with an angle given and you’ve just solved for one of the sides. Can you determine the length of x?

 

[Taryn]

its all good... I figured out my problem... I didnt read the question properly... and ended up figurin out the right answer, thanks for you time and help!