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Derive the formula for the electric potential energy of two point charges

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Consider a system of two charges containing two charges q1 and q2 fixed at two points A and B. AB=r1. Now q2 is taken from B to a new point C along AB and AC=r2

If the charge is displaced from r to r+dr then work done 

dw=F.dr

\\=\frac{Kq_1q_2}{r^2}.dr

total work done 

\\W=\int_{r_1}^{r_2}\frac{Kq_1q_2}{r^2}.dr\\=\frac{q_1q_2}{4\pi\ \epsilon_0}[\frac{1}{r_1}-\frac{1}{r_2}]

Change in potential energy 

U(r_2)-U(r_1)=-W

\\=\frac{q_1q_2}{4\pi\ \epsilon_0}[\frac{1}{r_2}-\frac{1}{r_1}]

Posted by

Safeer PP

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