PHYS208 Fundamentals of Physics II

Quiz 1

[4 charges on a square]

What is the direction of E experienced by the charge at point P?


Solution:

Since we have been asked about the electric field experienced by the +2Q charge,it may be treated as the positive test charge. The directions of the electric field contributions from the other three charges are indicated below:

[4 charges on a square]

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.

[4 charges on a square]

The relationship for the electric field of a point charge:  [E from a pt charge]

Thus the magnitude of the contribution from 1 (and 2) is

[result1]

and the resultant is

[result2]

The magnitude of the contribution from 3 is

[result3]

[result4]

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).


"http://www.physics.udel.edu/~watson/phys208/quiz1soln.html"
Last updated Sept. 13, 1997.
Copyright George Watson, Univ. of Delaware, 1997.