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Given two parallel wires carrying a current (e.g. 2 and 3 Amperes) and the distance between them, 5 cm, how do I determine the magnitude of the magnetic field at a point M mid-distance between the wires (2.5 cm from each)?

The wires are located in a vacuum with ${\mu}=4\pi10^{-7}$. If I use the formula $$B=\frac{\mu*I}{2*\pi*r}$$ and calculate the magnetic field for both currents/wires, how do I find the resulting magnetic field?

How do I do that, assuming the wires are perpendicular and in the same plane? How does this generalise to more than two wires?

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up vote 3 down vote accepted

The Maxwell equations are linear equations, which implies that a linear combination of solutions is a solution itself.

That is, if you know the magnetic field $\vec B_1$ arising from a current $\vec j_1$, and the magnetic field $\vec B_2$ due to a current $\vec j_2$, you know that the magnetic field in the presence of both currents, i.e. the current $\vec j = \vec j_1 + \vec j_2$, is just the sum of the magnetic fields, namely $\vec B = \vec B_1 + \vec B_2$.

This is a little harder to implement using your formula, as it only gives you the magnitude of the magnetic field and not its direction, but I am positive that you will be able to figure that out, using, for example, the Right Hand Rule on both wires to determine the direction of the magnetic field and then add the relevant components together.

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Actually, I was given a drawing too..I forgot to mention the direction of magnetic field :D. Thanks! – Transcendental Dec 8 '12 at 21:55

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