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When a unit positive charge (say A) is in the field of a unit negative charge (B) , it attracts A towards it. But when it moves towards B its potential energy changes to kinetic energy and by the time its in the new position its potential energy is reduced. My doubt is that if an external agent provides the energy to move the charge would it gain potential or will it remain the same?

  1. As in will its original potential energy remain unchanged and only the energy of the external agent will get used up?
  2. does the p.e remain the same since it is not doing work against any force?

Please forgive my mistakes and correct them, I'm a beginner.

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    $\begingroup$ The change in potential would remain the same even if the external agent acts on it. $\endgroup$
    – Harshit Joshi
    Commented Oct 23, 2018 at 11:44

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The change in potential is determined by the work done by the internal (i.e. electrostatic) field. External forces play no role.

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  • $\begingroup$ But isn't potential the force per unit charge? I do not get it. Do you mean to say that it doesn't matter if I throw a ball down or if the ball falls, the ball is still going to loose its potential? (I thought this is how it worked). Am I confusing potential energy with potential? $\endgroup$
    – Ikar
    Commented Oct 24, 2018 at 16:32
  • $\begingroup$ Potential is $V=-W_{\mathrm{internal}}/q$. Work, not force. And internal work. Consider two like charges. If allowed to move, they will move away from each other. The displacement and the force are in the same direction, so the work done by the internal force is positive. However, as they move apart, the potential at one due to the other decreases. So yes, it doesn't matter if you throw the ball or not. The potential is associated with the force of gravity (internal) not the force due to your hand. $\endgroup$
    – garyp
    Commented Oct 24, 2018 at 16:39
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The potential energy of charge A in the field of charge B is a function of the distance between the charges, $r$ $(U=k_e \frac {q_A q_B} r)$ and does not depend on how charge B has arrived to its position.

If charge B is moving from afar by itself (we assume that the charges have opposite signs and attract each other), its kinetic energy will increase at the expense of its potential energy.

If charge B is moved from afar by an external agent, it may transfer all or part of its potential energy to the agent, which will have to perform some negative work trying to keep the charge from accelerating.

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