If electricity creates a magnetic field, could a (strong) magnetic field stop electricity? Surely this would make the two magnetic fields interact and if movement was made impossible, the stronger magnetic field would block the weaker electromagnetic filed. Am I right (presuming that the magnetic field is stronger than the electromagnetic field created by the electricity)?
 A: There are a few things that need to be cleared:


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*now we know that there is a field called EM field, which unifies both electric and magnetic fields.

*the expression electric field and magnetic field is observer dependent, one observer might see the same field as magnetic, another observer as electric
So basically you are asking whether if there are two EM fields, will they conflict or interact with the field itself.
Now let's say you have two charges (electrons), they will create an EM field around themselves. These fields will affect both the other charges, that is when the EM field of one charge will interact with the other charge.
This is what we call the near field, and let's assume you are asking about that.
Basically you are asking whether two near fields affect each other. This would mean that the near fields, if they would have an edge, would affect each other without affecting the charge itself (from far away).
You are mistaking the interaction by assuming that the near fields will interact themselves, repelling in this case. It is not true. What creates the repulsive force between two electrons, is when the near field of one charge interacts with the other charge. And vica versa.
We use virtual particles in the mathematical description of the near fields, to describe the interaction, because truly, we do not know what or how interacts. 
You are asking whether when the edges of the near fields touch, will they repel, they will not. The near fields of the two charges themselves will not interact in this way. The interaction is always between the charge and another field.
The magnetic and electric fields are observer dependent, but let's assume you are asking from one observer's frame. Now if there is a magnetic field from this observer's view and another electric field, then you are asking whether the magnetic field (created by one charge) will affect the other charge (that creates the electric field). Yes it could affect it. But how could it stop it?
