How Do Currents in Perpendicular Wires Affect Magnetic Field Calculation?

[Ethers0n]

I want to calculate the magnitude of a net magnetic field. I've got two long wires. One that carries a current of 6.2 A in the positive y direction and the other wire has a current of 4.5 A in the positive x direction.

Is the resulting magnetic field the resulting vector when these fields are added using vector addition?

thanks

 

[StatusX]

Yes, and this is the principle of superposition, which is in fact necessary to get the field of a single wire, because you have to add the contributions from the current at each point along the wire to get the field at a given point.

 

[Ethers0n]

So, if I find the magnitude of the field from wire 1 and the magnitude of the field from wire 2 (say X and Y are the names of the wires) it's simply |X|^2 + |Y|^2 = (magnitude of the resulting field)^2 ?
That seems easy, I'm just wondering if I'm missing anything...

 

[jdavel]

Ethers0n,

, "...it's simply |X|^2 + |Y|^2 = (magnitude of the resulting field)^2 ?"

Is that vector addition?

 

[StatusX]

That would be true if the fields were perpendicular, but they aren't. The wires are perpendicular, but the fields circle the wires. For example, if you were to draw a square at the intersection of the wires (assuming they intersect; the non-perpendicular fields are even more obvious if they don't), then at the opposite corner of the square, the fields will actually be parrellel.

 

[Ethers0n]

StatusX
So are you saying that the magnitdues of fields are additive? Because the force lines are going in the same plane (but at orientations perpindicular to one another)?

 

[cAm]

additive, i think so. But, i do know that they are going in opposite directions... (right hand rule)

 

[StatusX]

The fields must be added as vectors. They are neither always perpendicular or always parellel. If you are restricting yourself to a specific point or region in space where they are perpendicular or parellel (eg, in the plane spanned by the wires, if they intersect, the fields are always parellel and perpendicular to the plane), then you can add them accordingly (as scalars if they are parellel or by the pythagorean theorem if perpendicular). But to find the field at any point in space, you need to find the three components and add them seperately.

You mentioned the force lines, but I'm not sure what you mean. Yes, force obeys the superposition principle too. But you don't know the force until you specify the velocity of the test charge; you can't calculate the force from the wires alone.

 

[jdavel]

Ethers0n,

You need to back up a little. Can you write an equation for the magnetic field produced by the current (4.5A) flowing in the positive x direction?