Calculating Magnetic Field Intensity Between Two Parallel Wires

[Winzer]

Homework Statement

Two long parallel wires are a center-to-center distance of 1.50 cm apart and carry equal anti-parallel currents of 1.80 A. Find the magnetic field intensity at the point P which is equidistant from the wires. (R = 4.00 cm).

Homework Equations

$$B= \frac{u_{0}I}{2\pi r}$$ infinite wire

The Attempt at a Solution

Ok I have been workin this problem for a while.
In terms of vectors, the y's cancel out.
For the X direction I get:
$$B_{totalx}=\frac{u_{0} I R}{\pi \sqrt( (d/2)^2 +R^2)}$$
I don't get why I am wrong, I took the sum of the b-fields in terms of vectors.
And no the answer is not 0 T!

 

[PiratePhysicist]

Why do you think that the Magnetic field is not zero?

 

[Winzer]

Thats what I thought originally , but it is incorrect.

 

[PiratePhysicist]

If they have equal, anti-parallel currents, and it's a point that's equidistance from the wires, then the answer has to be zero. Unless you decide to ignore the fact that magnetic fields are vectors.

 

[TVP45]

Anti-parallel.

 

[Winzer]

If they have equal, anti-parallel currents, and it's a point that's equidistance from the wires, then the answer has to be zero. Unless you decide to ignore the fact that magnetic fields are vectors.

Thats what I used to think too, but when I entered 0 T it is incorrect.
there is something else I am missing.

 

[Winzer]

Anti-parallel.

got an idea?

 

[TVP45]

Go back and ask your instructor what he means by anti-parallel. It has more than one meaning. It shouldn't but it does.

 

[Winzer]

I agree, word choice could be better.
However I don't have contact with my prof. right now, this assignment is due in an hour.

 

[PiratePhysicist]

If I was you I would give your best guess (ignore that you know it's "not right") and argue for points later. Chances are others having the same problem.

 

[sadakaa]

perhaps his answer is wrong by mistake? talk to other people in the class

 

[Winzer]

he is not, there is an answer I people got. There is some trick though, but my math tells me otherwise,

 

[nrqed]

If they have equal, anti-parallel currents, and it's a point that's equidistance from the wires, then the answer has to be zero. Unless you decide to ignore the fact that magnetic fields are vectors.

? The two B fields add up, they don't cancel!
It's when the currents are in the same direction that the total B field is zero at the point midway between them.

 

[Doc Al]

$$B= \frac{u_{0}I}{2\pi r}$$ infinite wire

Good.

The Attempt at a Solution

Ok I have been workin this problem for a while.
In terms of vectors, the y's cancel out.

True.

For the X direction I get:
$$B_{totalx}=\frac{u_{0} I R}{\pi \sqrt( (d/2)^2 +R^2)}$$
I don't get why I am wrong, I took the sum of the b-fields in terms of vectors.

Show how you got that answer--it's not dimensionally correct, for one.

 

[TVP45]

OK, now that I can see your diagram, I see the instructor used anti-parallel in the correct sense.