29 April 2010

Electrostatic point charges ranking task poll -- Here's the answer!

Electric field is a vector -- that means that a sum of many electric fields requires vector addition, with arrows.  Just adding up the values of kQ/d^2 does not work.  (I don't care how many times you say this, someone in your class will forget on a test or quiz.)

The electric field created by a point charge points (hah!) away from a positive charge, and toward a negative charge.

Electric field vectors, like all vectors, are best added by placing them tip-to-tail.

Consider diagram 1 in the ranking task.  The top charge creates a field to the right (away from the charge); the bottom charge creates a field up and to the right.  The vector sum of these electric fields is in red below:

DIAGRAM 1

Now consider diagram 2.  The top charge still creates a field to the right, but the bottom charge now creates a field down and to the left (toward the negative charge).  The vector sum of these fields is in red below:

DIAGRAM 2

From the picture, it is apparent that the magnitude of the electric field in diagram 1 is bigger than the magnitude of the electric field in diagram 2 -- the arrow for Etotal is bigger.

Similar reasoning for diagrams 3 and 4 gives the same sized total electric field vectors, but pointing the opposite directions.  Since the *magnitude* of an electric field means the amount of electric field, regardless of direction, we can say that diagram 3's field has identical magnitude to diagram 1's field; and that diagram 2's field is equal in magnitude to diagram 4's field.

Thus the answer:  (1=3), (2=4).