Question

Two positive charges of 2e-10 C are placed on the x axis at distances +40 cm and -40 cm from the origin, respectively. A third positive charge of 3e-11 C can be moved along the y axis. At what value of y the electrostatic force on the third charge is maximal?

Answer 1

ANSWER

First we have to rename the exercise information as following:

Then we begin with a drawing of the problem. This drawing below shows the forces on charge 3 due to charges 1 and 2. By symmetry, we can see that we will only be concerned with the y components, since the x components of these forces will cancel. We also see, by symmetry, that the y component of each force is the same.

Later, the net force on is the superposition of the forces from each of the two charges as follows:

So, if we se the figure above and find the values of and , we have that:

Thus, the electrostatic force will be:

Then, to find the maximum we take the derivative of F and set it equal to zero as follows:

Finally, solving for gives the value to the electrostatic force position at axis on the third charge is maximal:

   ANS.

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