Wednesday, September 2, 2015

In This House, Mom and Dad Make the Electric Field

In a family with two daughters, aged 3 and 6, the existence of household rules is pretty much a given.  My wife and I are probably lenient compared to many other parents, but maintaining a good environment at home does require some guidelines that the kids come to know.

As I was lecturing about the concept of an electric field yesterday, most of those who were awake were largely unimpressed by the rather abstract concept.  So, here is my attempt to make an analogy so the idea can sink in.

Let us consider my wife and I as "source charges" and our two children as "test charges".  Then, let's label our household rules our "electric field".

The source charges generate the electric field, and the test charges follow them, or go against them, depending on the sign of their charge.  Us parents make the rules, and if one of our daughters is feeling positive, or, agreeable, they follow them.  If she feels confrontational at a given moment, she will surely go against the rules, even if the rule is "eat this chocolate bar" (did I mention I have a 3-year-old?).

Those familiar with the concept of an electric field, realize that in the above analogy, the extent to which a rule is followed or not represents a force.  The relationship between the electrostatic force onto a test charge q in an electric field E is simply: F = qE.  The force onto a test charge within an electric field will either be in the direction of the field or exactly opposite to it.

It is appropriate to equate the electric field to an environment, because that is just what it is.  The rules of the house exist even when a child is not home to obey them or not.  Also, a field has a given direction and magnitude that varies in space.  The rule (direction) in the entrance-way is "take off your shoes when you come in the house," but it is kind of a soft rule that is defied on a daily basis.  "Don't hit your sister!" on the other hand, applies in all spaces and is associated with a large magnitude.  For that reason, when the rule is broken by a negatively charged child, the reaction to it is pretty serious.

A big point of contention in class whenever introducing this concept is "Why don't test charges affect the electric field?"  It is a matter of definition: the source charges establish the electric field - the equivalent to the standard reply "Because we're the parents and we say so."  When the kids grow up, maybe they can become small source charges in the house and have some say on the rules, but not yet.

By definition, an electric field at a given point in space indicates the hypothetical force that would act on a positive charge were it situated there.  Similarly, the rules of the house are made with the presumption that they will be followed by positively charged children.  Right.  My wife and I will need to take a close look at the field we generate, particularly as our little test charges become teenagers.

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