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Illustration Potential Energy of a Charge in a Radial Electric Field

Potential Energy of a Charge in a Radial Electric Field
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A test charge \(q\) is in the radial electric field of the source charge \(Q\). Both are positively charged and are separated by distance \(r\). The sample charge is located at the point \(P\). The reference point \(P_0\) of the potential energy is conventionally set to infinity, i.e. the distance of the reference point to the generating charge \(Q\) is infinite. The potential energy at the infinitely far position is zero by definition.

Thus, to bring a positive sample charge \(q\) from infinity to the point \(P\) (in the E-field), energy must be expended, which represents potential energy.