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Working with charges in equlibrium

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Hi. Can someone please walk me through the following problem?

Two point charge lie on the x axis. A charge of +9.9 micro-Coulombs is at the origin, and a charge of -5.1 micro-C is at x = 10.0 cm.
a) At what position x would a third charge q3 be in equilibrium?
b) Does your answer to part (a) depend on whether q3 is positive or negative? Explain.

Thank you!

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Step by step explanations with the final answer.

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Please see the attached figure..

For q3 to be in equilibrium, the force on it due to q1 must be equal and opposite to the force on it due to q2.

that is, F31 = - F32 ------(1)

Now, F31 = k * q1 * q3 /(0.1+x)^2

and F32 = k * q2 * q3 /x^2

Now from equation 1, we will write, ...

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