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Unformatted text preview: D 2q ( D + d ) 2 = q D 2 b 11 (1 + d D ) 2 B . Treating d/D as a variable (set x = d/D ) write down the Taylor expansion (Taylor Series) for the function inside the square brackets. Multiply the Taylor expansion by q/D 2 to obtain an expansion for E . Using the expansion you obtained, show that E is approximately 2 qd/ ( D 3 ) when P is far away from the dipole. Comment: The electric ±eld decays much more rapidly than the ±eld generated by one of the charges because the ±elds generated by each particle partially cancel one another. The approximation tells us the rate of decay....
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This note was uploaded on 05/08/2008 for the course MATH 126 taught by Professor Smith during the Spring '07 term at University of Washington.
 Spring '07
 Smith
 Exponential Function, Taylor Series

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