What is the direction of E experienced by the charge at point P?
Note that the magnitudes of the contributions from 1 and 2 are the same since charges 1 and 2 are the same. A direction has been assigned to the contribution from charge 3 [diagonally inward] but its magnitude relative to the others is not known until we evalutate it.
Recognizing that the resultant of the contributions from 1 and 2 points diagonally outward, as shown below, the solution to this question reduces to a determination of the relative magnitude of the contribution from charge 3 to the resultant of the contributions from 1 and 2.
|The relationship for the electric field of a point charge:|
Thus the magnitude of the contribution from 1 (and 2) is
and the resultant is
The magnitude of the contribution from 3 is
which is one-half that from 1 and 2 combined, so the relative contributions shown in the previous figure are correct and the direction of E from all three contributions points diagonally outward (225 degrees or southwest).