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On calculating the electrostatic potential at a point due to charge q, by definition, it is the work done to bring a unit positive charge from infinity to that point. Trying to find it mathematically, it should be

∞→R ∫E.dr where E = k* q/r*r

On evaluating the integral, i find a minus sign in the answer which is -kq/R. I have a few doubts regarding this.

1.Is potential energy the work done by external force against the electrostatic force or the work done by the electrostatic force itself.

2. If there is a minus sign in the work done, it should be the case where the work done is by the system, that is without any external force, the body must move from initial to final position yielding that amount of energy. Which cannot be the case with a positive charge if the source charge at the centre is also positive.

∞→R ∫E.dr where E = k* q/r*r

On evaluating the integral, i find a minus sign in the answer which is -kq/R. I have a few doubts regarding this.

1.Is potential energy the work done by external force against the electrostatic force or the work done by the electrostatic force itself.

2. If there is a minus sign in the work done, it should be the case where the work done is by the system, that is without any external force, the body must move from initial to final position yielding that amount of energy. Which cannot be the case with a positive charge if the source charge at the centre is also positive.

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