# A point in multiple magnetic fields

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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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 $\vec B = \vec B_1 + \vec B_2$.