# How do you calculate the resulting magnetic field for multiple sources?

I've been looking at some fusion reactors and I keep wondering how putting some kind of extra magnet in some configuration would affect the field, but I don't know how to figure it out. Like for example if you took a solenoid and sat a permanent magnet down next to it. This is the only thing I could find: https://www.quora.com/How-do-I-calculate-the-magnetic-field-created-by-a-number-of-magnets

Edit: I'm pretty sure it's just super positioning, but I need someone else to answer, because I don't know for sure. Also does it follow from Maxwells equations?

• In linear media (i.e., when you can assume vacuum permittivity and permeability), then the superposition of all the sources works great. Part of the problem is that you measure the total field so without other information, you cannot determine much about the individual sources from a single-point measurement. Commented May 19, 2017 at 20:33

$$\mathrm d\vec B = \frac{\mu_0}{4\pi}\frac{I \; \mathrm d\vec l \times \vec R}{R^3}$$
Maxwell's equations are linear ($\nabla \times$ and $\nabla \dot{}$ are linear operators) and it follows that solutions ($E$ and $B$) obey the superposition principle.