picture http://www.webassign.net/bauerphys1/23-p-056.gif Three charges,q1, q2, a

Question

picture http://www.webassign.net/bauerphys1/23-p-056.gif
Three charges,q1, q2, and q3,are all initially infinitely far apart, and will be brought one at a time to the corners of an equilateral triangle with side length of 7.9 m.

(a) Find the work done to bring the first particle, q1 = 8.0 pC, to P from infinity.
i got 0 j which is right but i have no idea why i just thought it would be 0 since work is something over distance and distance is too big so the answer would b 0 J
could someone explain?

(b) Find the work done to bring the second particle, q2 = 7.0 pC, to Q from infinity.


(c) Find the work done to bring the last particle, q3 = 1.0 pC, to R from infinity.


(d) Find the total potential energy stored in the final configuration of
q1, q2, and q3.

thank you

Explanation / Answer

Since the Coulomb force F = kq1q2/r2 and work is force times distance, the work to bring one charge in from infinity towards another is the coulomb force integrated over distance (negative since we are operating against the force):

-kq1q2 dr/r2 = kq1q2[1/r] since we take the integral from infinity to r. This also is the formula for potential energy between two charges.

part (a): 0 J because there is no force to work against, there is no other charge

part (b): (8.99 *109 Nm2/C2)(8 * 10-12 C)(7 * 10-12 C)/(7.9 m) = 6.37 * 10-14 J

part (c): (8.99 *109 Nm2/C2)(8 * 10-12 C)(1 * 10-12 C)/(7.9 m) = 9.10 * 10-15 J plus a second piece,

             (8.99 *109 Nm2/C2)(7 * 10-12 C)(1 * 10-12 C)/(7.9 m) = 7.96 * 10-15 J

part (d) add all three pieces together, 8.08 * 10-14 J

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