E and B

Physics students learn about the electric field vector E and the magnetic field vector B. In most courses these vectors are taught separately with E introduced first as being produced by a stationary charge and B introduced later as being produced by a moving charge. A common mindset is to consider these fields to be different, just because of the order in which the courses are taught, but fundamentally they are not. They are both aspects of the electromagnetic field and become active in particular situations. In SI units E and B have different measurement units and this tends to cloud their difference. In CGS units E and B have equivalent units and so this system is more suited to electromagnetic calculations as the numerical values of the fields can be directly compared. Many physics students do not realise that electromagnetism is a direct consequence of Einstein's special theory of relativity, as Einstein's 1905 paper on relativity was entitled 'On the Electrodynamics of Moving Bodies'. There is no better way of expressing the relationship of electromagnetism to relativity than the following  marvellous quote given by Leigh Page, then professor of mathematical physics at Yale, in an address to a meeting of the American Institute of Electrical Engineers in 1941.

The rotating armatures of every generator and every motor in this age of electricity are steadily proclaiming the truth of the relativity theory to all who have ears to hear

Some Mathematical Meandering II

Here is a beautiful problem. This problem starts with a minimum of assumptions and soars to great heights in its simplicity of solution using high school calculus. It is called a "marvellous problem" by Carl M Bender and Steven A Orszag on page 33 of their legendary book Advanced Mathematical Methods for Scientists and Engineers. Now be warned. Once you are captured by this problem its beauty could lead you on mathematical travels to distant places. Here is the Snowplow Problem.

One day it started snowing at a heavy and steady rate. A snowplow started out at noon, going 2 miles the first hour and 1 mile the second hour. What time did it start snowing?

11 :23 AM