| E-M Home Page/Unit 1/ | First Created 9/2/02 |
Unit 1 - Fields |
What is a field? Actually, in the physical sciences you may encounter two barely-related technical meanings of the word, both distinctly separate from both the agricultural uses and such uses as "field of study".
The one we are not concerned with here, and this paragraph is all I plan to say about it (and even this is possibly oversimplified) is that in mathematics, a field is a number system in which virtually all of ordinary arithmetic has its equivalents. The real numbers and the complex numbers are the two examples of fields that are familiar to the most people (though not necessarily under this label), but there are many others, of several types.
In physics and related subjects, a field designates the values at different places of a particular physical quantity. In other words, a field is given by a function whose input (argument) is a position variable and whose values are a single type of physical quantity. Realistically, and in part because of recognition that physical quantities are generally less than perfectly precisely determined, we normally assume fields are continuous, but sometimes we will discuss idealizations which would be described by discontinuities in a field.
Your first-year course will have introduced the electric field, but it probably did not spend much time on why. The strongest argument, perhaps, arises from the conclusions of the theory of special relativity, though it was implicit in electromagnetic equations already: if we move a charge here now, its effect on another charge cannot and will not appear instantaneously. But between our moving this charge, and the other charge moving later, what is keeping track of the change? Another aspect of this argument, perhaps, or perhaps it's an independent consideration, comes from our recognition that light, which moves, is an electromagnetic phenomenon, carrying energy and momentum (as we will discuss), but it does not consist of charges; what does it consist of?
In simplest terms, a field is used to replace the concept of direct action at a distance (as opposed to contact action, and which is problematic in relativity theory), the idea that one object at one place (and time) causes an effect on another object at a different place (and time). We replace it with a two- (or later three-)stage action: the first object causes a field simply by having an appropriate property (such as electric charge). Then the field acts on the second object according to the nature of whatever kind of field it is. (In the three-stage picture, we particularize some more: the source object causes certain characteristics in the field at its location; the field acts on the other object according to the field values at that object's location. In between, the values of the field at different places and times are interrelated by "field equations", which thus describe how the cause and the effect, being at two places, are related.
Again, your first-year course probably didn't emphasize this, but you were actually dealing with a field as early as when you discussed projectiles. I'm sure you remember the value "9.8 m/s2, down" associated with Earth's gravity. If you stop and think about it, even without considering the magnitude fluctuations that are of great interest to geophysicists, this quantity in Texas and in New South Wales are different, because "down" in Texas and "down" in New South Wales are nearer to being opposite than to coinciding. Thus, the quantity you use for acceleration in projectile problems is a field; in fact, it is the Earth's gravitational field. (Yes, you've studied gravitational field theory, even though you didn't know it by that name at the time. You can now brag about it, if you want, like the man who learned, and thereafter allegedly boasted, that he had been talking prose all his life.)
Another easy example of a field arises if we consider what a weather forecast map can indicate with colors: as a map, it conveys information about different places; with color, it can express a physical quantity such as a temperature reading. Thus, such a map could be displaying predicted values of a temperature field: temperature as a function of position.
Format for this page adapted with permission from pages
constructed by Dr. Lionel D. Hewett for his course
Modern
Physics 1.