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  1. There is a short dipole $ X,Y$ of charge $+q$ and $-q$ placed along the x-axis and then we consider the point at $A$ which is far away from the dipole and lies on the x-axis. The electric field $E_\text{net}$ experienced at that point will be $E_\text{net}=E_\text{XA}+E_\text{YA}$ where the $E_{ij}$ are vectors. The dipole charges also interact with each other. Why are we only considering the interaction between the dipole and the unit postive test charge at the point $A$?

  2. Would it be the same if we did the following? Keep a positive charge $+q$ at the origin and another positive charge at a distance far away on the x-axis. After that, introduce a negative charge $-q$ near to the origin. Will this result in the same configuration (in terms of electric fields) as in the previous case?

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  1. If you want to know the electric field strength at point A due to the point charges at X and Y, you do not need to know the strength of the electric force between the charges X and Y because this interaction does not affect the strength of the interaction which each of X and Y have at A. The charge at X exerts the same force on A regardless of where Y is placed. It is not weakened by interacting with the charge at Y.

Electric field is not like the flow of water from a tap. Assuming the tap cannot be opened further to increase the flow (litres per second), if more water flows from X to Y then there is less available to flow from X to A. If you remove the connection to Y then all of the water can flow to A, making this flow "stronger" (more litres per second).

  1. Yes the force on A would be exactly the same if the charges at X, Y and A are put into position in the order X, A then Y or A, Y then X, etc. The electric field does not have a memory of what happened previously. It only depends on the final configuration.

Both observations are summarised by the Principle of Superposition which applies in all linear systems. This says that the effect of a combination of 2 things X and Y is the sum of the effect of each of X and Y acting separately, as though the other were not there at all. Their effect on other objects is not changed at all by their effect on each other.

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