Two charges, X and Y, are placed along the x-axis. Charge X is +18 nC and is placed at x = 0. Charge Y is placed at a location of 0.60 m and has a charge of –27 nC. Charge Z of unknown positive charge is to be placed at some point along the x-axis so that it is at equilibrium. Find the position that Charge Z should be placed.

Charge Z can be placed at x = -2.7 m or at x = 0.27 m.

Explanation:

The Coulomb force between two charges, and , separated by a distance, , is given

k is a constant.

For the charge Z to be at equilibrium, the force exerted on it by charge X must be equal and opposite to the force exerted on it by charge Y.

It is to be placed along the x-axis. Hence, it is on the same line as charges X and Y.

Let the charge on Z be Q. It is positive.

Let the distance from charge X be x m. Then the distance from charge Y will be (0.60 - x) m.

Force due to charge X

Force due to charge Y

Since both forces are equal and opposite,

Applying the quadratic formula,

or

Charge Z can be placed at x = -2.7 m or at x = 0.27 m

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the entire statement is true and correct.  

there's no diagram, nothing is illustrated, and no question is asked.