HRW Problem 23.12

The plan is to add up the three forces as vectors. Since two of these cancel, we only have to find the last one using Coulomb's Law.

First we find the distance from the charge 2q to the point P using the Pythagorean theorem.

Then the force is simply:

HRW Problem 23.13

The plan is again to add the vectors as forces.

We can take advantage of cancellation by noting that all horizontal components cancel. Also, we notice that all vectors are at 45 degrees from some axis and so each component is multiplied by sin(45).

The up direction is taken to be positive.