Two point charges (+9.0 nC and -9 nC) are located 8.00 cm apart. Let U = 0 when all of the charges are separated by infinite distances.  What is the potential energy if a third point charge q =...

Two point charges (+9.0 nC and -9 nC) are located 8.00 cm apart. Let U = 0 when all of the charges are separated by infinite distances.

 

What is the potential energy if a third point charge q = -3.2 nC is placed at point b?

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You have not mentioned where the point b is where the charge q = -3.2 nC is placed.

For a charge q placed at a distance r from a charge Q, the potential energy is equal to U = kQq/r, where k is the Coulomb's constant.

In your question if q is at a distance Ra from the 9 nC charge and a distance Rb from the -9 nC charge, the potential energy of the charge q would be:

k*9*10^-9*(-3.2*10^-9)/Ra + k*(-9*10^-9)*(-3.2*10^-9)/Rb

= -k(28.8*10^-18)/Ra + k(28.8*10^-18)/Rb

= 28.8*10^-18*k*[1/Rb - 1/Ra]

This would be equal to 0 if Ra = Rb and the charge does not have any potential energy due to the oppositely charged particles. For all other values of Ra and Rb, the charge has a net potential energy.

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