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Considering the image we observe the following: $r_A<r_B \Rightarrow \frac{1}{r_B}<\frac{1}{r_A} \Rightarrow \frac{K(+Q)}{r_B}<\frac{K(+Q)}{r_A}$ (if $0<Q$) and thus

$$\frac{K(+Q)}{r_B}=V(B)<V(A)=\frac{K(+Q)}{r_A}$$ But we also know that the electric potential energy in a point $P$ is defined as $V(P)=\frac{U}{q_0}$, so if we consider a charge $+q$ where $q>0$ we have: $$U_B<U_A$$ Does that mean that the "potential energy of $+q$" is lower if $+q$ is far from the charge $+Q$ and higher if it's close? Now, if we consider $+Q$ and $-q$ where $Q>0$ and $q>0$then we have: $$U_A<U_B$$ Does that mean that the "potential energy of $-q$" is higher if $-q$ is far from the charge $+Q$ and lower if it's close? Now if we consider $(-Q),Q>0$ we have: $$\frac{K(-Q)}{r_A}=V(A)<V(B)=\frac{K(-Q)}{r_B}$$ Again, if we consider a charge $+q$ where $q>0$ we have: $$U_A<U_B$$ Does that mean that the "potential energy of $+q$" is higher if $+q$ is far from the charge $-Q$ and lower if it's close? And finally, if we consider a charge $-q, q>0$, we have: $$U_B<U_A$$ Does that mean that the "potential energy of $-q$" is lower if $-q$ is far from the charge $+Q$ and higher if it's close? enter image description here

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Does that mean that the "potential energy of $+q$" is lower if +q is far from the charge $+Q$ and higher if it's close?

The potenial energy for a point is given by: $$V_p(r)=k_e\frac{qQ}{r}$$

where:

$$k_e=\frac{1}{4\pi \epsilon_0}$$

The value of $V_p$ does depends on:

  1. the scalar values of $q$ and $Q$
  2. if both charges are of equal sign then $V_p$ will be positive valued
  3. if both charges are of opposite sign then $V_p$ will be negative valued.
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The potential energy of the charge q at point A in the field is equal to the work required to move it to that point from an infinite distance* ($U = -\int_{\infty}^{\mathbf{r}_A} q \mathbf{E} \cdot d \mathbf{r} = \frac{1}{4 \pi \epsilon_0} \frac{Q q}{r_A}$). For like charges (+Q, +q or -Q, -q) this will be positive and decrease with increasing distance. For unlike charges (-Q, +q or +Q, -q) this will be negative and increase with increasing distance.

*The reference point implied by the formulae you cite.

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