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Suppose three positive point charges are situated at the vertices of an equilateral triangle (as shown in fig). We can calculate the potential energy of this system which is

$$U_{total}= U_{AB}+U_{BC}+U_{AC}$$

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Now with two charges fixed (say charge A and B), the third charge C is released free. So we can calculate its kinetic energy when it goes far away from the two remaining charges. And this is equal to the potential energy that this charge shared with the two charges A and B namely $U_{AC}$ and $U_{BC}$ ... i.e.

$$k_C = U_{AC}+U_{BC}$$

But my question is that since the potential energy between two charges is stored in the space between them then why can't the charge at C take away some of the potential energy of the system of charges A and B i.e. $U_{AB}$? What prevents this "theft" of energy from happening?

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But my question is that since the potential energy between two charges is stored in the space between them then why can't the charge at C take away some of the potential energy of the system of charges A and B i.e 𝑈𝐴𝐵 ? What prevents this "theft" of energy from happening ?

In principle nothing stops it. That can happen. Such forces which behave in that way are called three-body forces.

https://en.m.wikipedia.org/wiki/Three-body_force

Electromagnetism is not such a force, so you cannot get that effect using EM. However, the strong nuclear force does show evidence that it is a three-body force (or even higher).

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We need to specify what the signs of the charges and potentials are. Secondly, potential is always specified relative to a reference. If you have two oppositely charged particles some distance apart, then the potential from infinity is negative (we got work out of the system by allowing them to move closer) and positive relative to them being closer (we had to do work to move them further).

The potential is not exactly “stored in the space between them” it is in the situation as a whole. It is the work needed to assemble this. Work is force times distance (actually integral of F dt).

Let’s just assume all three charges are the same sign (all positive or all negative). Then to assemble this situation, moving the particles from being far apart, took work (energy), and by conservation of energy that work has become potential energy (which is energy we can get out of this system if we want, one way being as kinetic energy, another way being as work which could create a variety of kinds of energy). It’s the same work as to set-up just AB plus just AC plus just BC. And if we let the particles go, then they would gain velocity and it would be kinetic energy.

If C is of opposite charge, then U_ac and U_bc are negative. So the total could be reduced by that. The equation would still stand. That would mean removing C would not get us any energy but would take further work. We gained energy by letting it move into this system, which is negative potential.

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For your system of charges we need to know the signs of the charges to determine the total potential energy. Let's assume are all positive point charges.

Starting with one charge fixed in position (say $Q_A$), the total potential energy is the sum of the work required by an external agent to bring each of the other charges (say $Q_B$, followed by $Q_C$) from $\infty$ to its position with respect to the other charge(s). The total potential energy is then

$$U_{tot}=\frac{1}{4\pi\epsilon}\biggl (\frac{Q_{A}Q_{B}}{r_{AB}}+\frac{Q_{A}Q_{C}}{r_{AC}}+\frac{Q_{B}Q_{C}}{r_{BC}}\biggr )$$

But my question is that since the potential energy between two charges is stored in the space between them then why can't the charge at C take away some of the potential energy of the system of charges A and B i.e $U_{AB}$ ? What prevents this "theft" of energy from happening ?

The potential energy between two charges is not stored in the space (electric field) between them. It is stored in the system of each pair of charges and the electric field between them.

You can think of the total potential energy of the system of three charges as the sum of the potential energies of three subsystems, or

$$U_{sys}=U_{AB}+U_{AC}+U_{BC}$$

Where

$$U_{AB}= \frac{Q_{A}Q_{B}}{4\pi\epsilon r_{AB}}$$ $$U_{AC}= \frac{Q_{A}Q_{C}}{4\pi\epsilon r_{AC}}$$ $$U_{BC}= \frac{Q_{B}Q_{C}}{4\pi\epsilon r_{BC}}$$

Since the potential energy of each subsystem is energy shared by the pair of charges and the field between them, if charge $Q_C$ is freed from its position to convert to kinetic energy, it takes with it the potential energy that charges $Q_A$ and $Q_B$ shared with it.

What you are calling "theft" is simply the loss of part of the potential energy of the initial system of charges due to the removal of whatever constraint is involved to keep one or more of them fixed in place. What "prevents" this "theft" is some external agent keeping the charges from moving away from each other due to repulsion, converting potential to kinetic energy.

Hope this helps.

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The reason is the linearity of the Maxwell equations. Each charge feels the sum of the electric fields of the other two. Therefore the work to remove C to infinity is the sum of the work required due the field of A and of B. The work due to A does not depend on the presence of B and vice versa.

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