Does Integration Imply Superposition in Field Calculations but Not in Energy?

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The discussion centers on the relationship between integration and the principle of superposition in field calculations versus energy calculations. It questions whether the integration methods used for continuous mass and charge distributions imply superposition, particularly in field calculations. The key point raised is that while fields can be superimposed, energy calculations do not follow the same principle due to the nature of squaring values. Specifically, the square of a sum differs from the sum of squares, leading to discrepancies in energy calculations. This highlights a fundamental distinction in how fields and energy are treated in physics.
Kolahal Bhattacharya
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While calculating field and potential due to a continuous distribution of mass and charge,we use the standard methods of integration.Does it imply the validity of principle of superposition?If it does,then why we do not see it in the case of calculation of energy of the same distribution?
 
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The energy is proportional to the square of the field. Square of the sum is not always equal to sum of the squares.
 

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