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Introductory Physics Homework Help
Electric Dipole Potential Energy Calculation
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[QUOTE="arpon, post: 4988359, member: 526026"] [h2]Homework Statement [/h2] An electric dipole consists of two charges of equal magnitude ##q## and opposite sign, which are kept at a distance ##d## apart. The dipole moment is ##p= qd## . Let us next place two such dipoles, placed at distance ##r## apart, as shown in the accompanying figure. [ATTACH=full]78257[/ATTACH] a) Assuming that the potential energy for the charges while at infinity is zero, find the exact potential energy of the configuration in terms of ##d, r, q ## and fundamental constants. b)When ##d<<r## , approximate your previous result in terms of ##p, r ## and fundamental constants. [h2]Homework Equations[/h2] ##V = \frac {1}{4\pi \epsilon_0} \frac{q}{r}## ##W = Vq## [h2]The Attempt at a Solution[/h2] For the positve charge of A dipole, I calculated the potential energy ##= +q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d}) ##, because, ##W = Vq## The potental energy for the other three charges are the same. So, the potential energy of the configuration is ## = 4q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d})## ##= \frac{q^2}{\pi \epsilon _0} (- \frac{1}{r} + \frac {1}{\sqrt{r^2 +d^2}} - \frac{1}{d})##; Then , I can't find any way how to approximate the result when ##d << r##; In this case, I substituted ##r^2## for ##r^2 + d^2## ; So, two of the terms in bracket are cancelled. Then I plugged in ## q = \frac{p}{d}## ; But, still ##d## is there. [/QUOTE]
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Electric Dipole Potential Energy Calculation
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