P25_023 - r ) − 2 ( − d ) = 1 r + d r 2 . Similarly, 1...

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23. A positive charge q is a distance r d from P , another positive charge q is a distance r from P ,anda negative charge q is a distance r + d from P . Sum the individual electric potentials created at P to Fnd the total: V = q 4 πε 0 · 1 r d + 1 r 1 r + d ¸ . We use the binomial theorem to approximate 1 / ( r d )for r much larger than d : 1 r d =( r d ) 1 ( r ) 1 (
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Unformatted text preview: r ) − 2 ( − d ) = 1 r + d r 2 . Similarly, 1 r + d ≈ 1 r − d r 2 . Only the Frst two terms of each expansion were retained. Thus, V ≈ q 4 πε · 1 r + d r 2 + 1 r − 1 r + d r 2 ¸ = q 4 πε · 1 r + 2 d r 2 ¸ = q 4 πε r · 1 + 2 d r ¸ ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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