Friday, September 11, 2015

Newton's Third Law: "I Can't Stop Pushing Back!"

At some point in my thirties, I injured my shoulder playing soccer; it slammed to the ground after a nasty tackle in my 'friendly' soccer league.  After some nagging from my wife and a few of my students (who got to see what my left hand writes like at the board), I went to get some X-Rays of my right shoulder region taken.

Once in the room with the young radiologist, I was shown where to stand, somewhere between an emitter and receiver of the X-Rays.  She needed to make slight adjustments to my position between exposures.  She would place her hand on my shoulder and/or hip, and push or pull me to the right spot.  And each time it was time to move me, she would state, "Sir, please let me move you."  Eventually, this became, "Sir, please relax and let me move you."  Her frustration seemed to grow as she finally uttered, "Sir, please stop resisting being moved."

I must say, throughout all of this, it took every ounce of my patience to not say: "Enough! I can't take it anymore! Let me explain some basic laws of mechanics to you..."

First off, you cannot push or pull me without being pushed or pulled yourself.  That is Newton's third law, which, if ever violated, would send shock waves through the scientific community.  So, if you expect to push or pull me without getting pushed or pulled back, you must be new at this job.

Second, the extent to which I push back when you push me is related to my inertia.  The amount that you accelerate me from rest with your force has a limit.  It is not a matter of "relaxing my muscles" - the only way you will feel no resistance is if I have no mass.  By saying "Stop resisting being moved," you are essentially telling me to "Stop having mass."

In the end, I thought it would be smart not to lecture the radiologist about Newton's Laws of Motion.  I held back my urge to scream "Have you never heard of Isaac Newton?"  After all, she was in charge of the amount of high-frequency electromagnetic waves that would be periodically travelling through my body.  She could have responded, "Have you never heard of James Maxwell?"

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.