What is the principle of superposition of magnetic fields?

Vector magnetic field

So, the magnetic field is a vector field. This means that at each point in space, this field forms a vector, and not just a scalar value. That is, the magnetic field at any point in space acts in a certain direction. Thus, it is possible to specify a set of directed segments that form a field. If you graphically depict such a field, it will represent a large (or even infinite) number of vectors forming a single vector field.

Superposition property of magnetic field vectors

If the magnetic field is a vector, then all properties of vectors should be applicable to it. One of the most important properties of vectors, which even defines the very concept of a directed segment, is the possibility of summing vectors. That is, if there are, say, two vectors, then there always exists a third one, which is the sum of the first two vectors.
In this case, we are talking about magnetic field vectors. Therefore, it is supposed to summarize the magnetic induction vectors, and by the sum we mean a complete or superpositional field, which can replace the set of fields of its components. Thus, the principle of superposition states that the induction of a magnetic field created by several sources at a given point in space is equal to the sum of the magnetic fields created by each of the sources separately. Now it becomes clear that the vector sum of fields is assumed. It is important to note that they mean not the sum of the vectors of this vector field, but the sum of the vectors of different vector fields created by different sources, but at one point.
This principle makes it possible to calculate the magnetic fields in difficult situations is incredibly simple. Knowing the distribution of the magnetic field of any elementary sources (conductor with current, solenoid, etc.), any necessary magnetic field can be constructed from such simple elements, whose field can be calculated using the principle of superposition of magnetic fields.
The most important consequence of the principle of superposition of magnetic fields is the law of Bio-Savart-Laplace.This law generalizes the principle of superposition to the case of infinitely small vectors making up the full field. In this case, summation is replaced by integration over all infinitely small magnetic induction vectors. Such elementary induction vectors are usually conductor currents. Thus, the integration (summation) is conducted along the entire length of the conductor through which current flows.

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