A Charge -Q is located at (-1,1), while a second charge, 2Q, is located at (1,2)

Question

A Charge -Q is located at (-1,1), while a second charge, 2Q, is located at (1,2). A. What is the total force acting on a test particle, q(not), located at the origin? B. Locate a point, giving x- and y- cordinates, where the force is zero. If it will never be zero anywhere in this system, please indicate that. C. If the test charge is moved from the origin to the point (5,5), how much work is done by the electric force? I'm going back through one of my old tests and I keep getting this one wrong. For some reason my x hats cancel out and it completely messes everything up! A complete solution, not just the answer, would be greatly appreciated :)

Explanation / Answer

A.force on the test charge q = F1 F2 F =- KqQ/ 2 + Kq(2Q) / 5 = -KqQ/10 where K =1/ 4 X pi X epsilon nod. C work done by electric force = F net X distance. = KQq/ 10 X 7.07 = 0.707kqQ J B. there is no point where the force can be zero as the charges are assisting each other when a test charge is brought between them or anywhere near them.

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