Potential Energy between charges

Question

A positive charge of 3 nC is placed at the origin and a positive charge of 6.75 nC is
placed on the x-axis 5 cm. A positive test charge of 2 nC is placed on the x-axis a
distance d, between these two charges.

 

When the test charge is placed at 2cm what is the force and the potential energy at this point?

 

The Force is 0N i am 100% sure.

 

I have tried to work out the potential energy but my answer differs from the one provided. My attempt is

 

 U = ∑ kQ₁Q₂/r

 

Doing the sum of these I got my answer to be 6.74x10^-6 J

 

The answer provided is 2.74x10^-6 J

Answer 1

Ian; Your equation and numbers all look good to me. The total PE is either the sum or difference of the individual 2 PE's and the sum is what you have. It is possible the provided answer is wrong. Recall that scalar functions like PE just add/subtract while vector functions like Force add vectorially. Your sum answer is 6.75e-6 Joules. The difference answer is 1.35e-6 Joules. And 2.7e-6 is the PE between the 2nC and 3nC charges.