Total field, scatt field, incident field

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In scattering problems, the total field is defined as the sum of the incident and scattered fields. However, when a scatterer is impacted by an incident field, it re-emits energy in various directions, leading to questions about the necessity of the incident field in calculating the total field. If the incident field is absent, the total field consists solely of the scattered field. This indicates that the presence of the incident field is not always required for the total field to exist. Thus, the total field can vary depending on the presence or absence of the incident field.
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total field, scatt field, incident field...

in scattering problems, there is this formulation

total field= incident+ scattered

But once a scatterer is hit by an incident field, it re-emits, re-radiates in different directions.
Why should the field at a particular place always have to be the sum of the scattered and the incident? maybe the incident is not there?

We are like assuming that the incident field moves across the scatterer as if the object was not there. Then the scattered field modifies the incident field to get the total field...

Behind the scatterer, I would, for instance just see scattered field...
 
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Yes, that is correct. When the incident field is not present, the total field is only composed of the scattered field. The incident field only adds to the total field when it is present.
 
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