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In addition, the magnetic field at a point depends upon how far the point is from the current element.
The value of the magnetic field at a point in the surrounding space may be considered the sum of all the contributions from each small element, or segment, of a current-carrying conductor.
Knowledge of the value of the electric field at a point, without any specific knowledge of what produced the field, is all that is needed to determine what will happen to electric charges close to that particular point.
In the first place, the value of the magnetic field at a point is directly proportional to both the value of the current in the conductor and the length of the current-carrying segment under consideration.
The value of the electric field at a point in space, for example, equals the force that would be exerted on a unit charge at that position in space.
For instance, with a very long straight wire carrying current, the value of the magnetic field at a point nearby is just directly proportional to the value of the current and inversely proportional to the perpendicular distance from the wire to the given point.
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As a result, the interpolating fields at a point depend exclusively on the nodal values within the region of influence.
One way to handle this situation and one of the starting points for axiomatic reformulations of QFT is not to consider fields at a point but instead fields which are smeared out in the vicinity of that point using certain functions, so-called test functions.
With the assumption of a quasi-uniform source, the impedance (transfer function, TF, relating electric to magnetic fields at a point on the Earth's surface) is well defined and independent of the actual (large-scale) spatial structure of the source fields.
Fig. 3 Absolute values of the full-loop (lowermost, blue), leakage (middle, red) and total (uppermost, black) magnetic fields at a point of observation located at 5 km east of a south-north railway as functions of time produced by a train travelling from south to north.
Moreover, since these conditions are in terms of the value of the vector field on each domain at a point, they are remarkably easy to verify.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com