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

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.