Two point charges $$q1$$ and $$q2$$ are placed in an external uniform electric field as shown in figure. The potential at the location of $$q1$$ and $$q2$$ are $$V1$$ and $$V2$$, respectively. The effect of $$q1$$ and $$q2$$ is not included in $$V1$$ and $$V2$$, i.e., $$V1$$ and $$V2$$ are potentials at location of $$q1$$ and $$q2$$ due to external unspecified charges only. Then electrical potential energy for this configuration of two charged particle is

Question

Two point charges $$q1$$   and  $$q2$$ are placed in an external uniform electric field as shown in figure. The potential at the location of $$q1$$   and  $$q2$$ are $$V1$$   and  $$V2$$, respectively. The effect of $$q1$$   and  $$q2$$ is not included in $$V1$$   and  $$V2$$, i.e., $$V1$$   and  $$V2$$ are potentials at location of $$q1$$   and  $$q2$$ due to external unspecified charges only. Then electrical potential energy for this configuration of two charged particle is

Infinity Learn · Accepted Answer

The potential energy of the system can be found by computing the work done by external agent in assembling the system without changing the kinetic energy of the system. Let us first bring q, from infinity to the desired location, then in doing so we have to do work against external electric field which is equal to $$W1=q1V1$$  (potential$$ at infinity is considered as $$zero). Now, we will bring $$q2$$ from infinity to the desired location, to do so, we have to do work against external electric field and against electric force of $$q1$$ so work done is $$W2=q2V2+q1q24$$πε$$0r$$ So total work done $$isU=q1V1+q2V2+q1q24$$πε$$0r$$

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