[![enter image description here](https://i.stack.imgur.com/Rdip2.jpg)](https://i.stack.imgur.com/Rdip2.jpg)Recently I got stuck witht the following problem. 

Imagine we have uniform a magnetic field which induction points upwards. The fields strength is steadily decreasing. If we put an iron coil perpendicular to the magnetic induction vector, then, obviously, there will be electric current induced in the coil. 

However, as I understand, the coil itself is only a 'marker' that displays the electric field lines that actually make the electrons move. It means that the elcetric field is there even when there is no coil. 
Now the problem:
I can imagine some coils being close to each other. It will essentially mean, that it in one of them the current will go one way and in the other - the opposite. How can this possibly be?

I looked at [this answer](https://physics.stackexchange.com/questions/8279/what-is-the-direction-of-the-induced-e-field-from-a-changing-uniform-magnetic-fi) as it is phrased very close to what I want and still I couldn't get the idea. Could the answer be presented in more layman terms .
['https://physics.stackexchange.com/questions/326104', 'https://physics.stackexchange.com', 'https://physics.stackexchange.com/users/89976/']
Since the Maxwell's equations are linear partial differential equations, you can compute the magnetic field due to multiple sources by superposition. 

A really important application relies on the superposition principle for magnetic fields is the Biot–Savart law i.e. the fact that the magnetic field is a vector sum of the field created by each infinitesimal section of the wire individually.

                                              ![enter image description here](https://i.stack.imgur.com/j8HaR.png)

$$\mathrm d\vec B = \frac{\mu\_0}{4\pi}\frac{I \; \mathrm d\vec l \times \vec R}{R^3}$$
You are correct, they follow superposition. The magnetic field is a vector field, and so they follow a vector sum when they are in a superposition.

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.