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Two charges q= +2.0 *10^6 are fixed in space a distance d=2.0cm apart . A.With V

ID: 2119746 • Letter: T

Question

Two charges q= +2.0 *10^6 are fixed in space a distance d=2.0cm apart . A.With V=0 at infinity, what is the electric potential at point?B.You bring a third charge q=+2.0*10^6 from infinity to C. How much work must you do ?

C. what is the potential energy U of the three charge configurationn when the third charge is in place?

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

Explanation / Answer

initial potential energy= (9*10^9)*(4*10^12)/(.02*.02) = 9*10^25 J

final potential = ((9*10^9)*(4*10^12)/(.02*.02))+2*(9*10^9)*(4*10^12)/(.01^2) = 8.1*10^26 J

work done = final -initial = (9*10^25)-(8.1*10^26) = 7.2*10^26 J

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