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Introductory Physics Homework Help
Approximating the force on a dipole Taylor series
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[QUOTE="Zack K, post: 6118326, member: 586916"] [h2]Homework Statement [/h2] Show that the magnitude of the net force exerted on one dipole by the other dipole is given approximately by:$$F_{net}≈\frac {6q^2s^2k} {r^4}$$ for ##r\gg s##, where r is the distance [B]from one dipole to the other dipole[/B], s is the distance [B]across one dipole[/B]. (Both dipoles are of equal length and both have charges of magnitude q). [h2]Homework Equations[/h2] ##F=\frac {kq_1q_2} {r^2}## ##f(x)=\sum_{n=0}^\infty \frac {f^{(n)}(0)} {n!} x^n## [h2]The Attempt at a Solution[/h2] I worked out the net force that a dipole would be acting on another as: $$F_{net}=kq^2(\frac {1} {(r-s)^2}+\frac {1} {(r+s)^2}-\frac {2} {r^2})$$ This equation is right because I plugged in values for r and s given r is much greater than s, and got the same value for if I used the approximated equation at the top. I just lack the knowledge of using a taylor series to approximate my equation into the desired one. [/QUOTE]
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Approximating the force on a dipole Taylor series
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