Decades ago, Tolly
Holt flew me to Germany to give lectures at a conference at the university in
Bonn. In one of my three lectures, I wrote up Faraday’s Law of induction on
the board; v = -d(phi)/dt.
I then said that, without any discussion, the text books followed this with
the formula (Integral)Eds
= -d(phi)/dt. I said that this step was illegal. Although I was only seconds into the
start of my lecture, I was immediately interrupted by professors and
lecturers present, who were appalled. A lengthy discussion followed. I said that if a loop of wire with a
single break was put around the perimeter of the surface under investigation,
a voltage drop could be measured. However, how would one measure the voltage
drop between two points some way away from each other along the loop? It
became clear that the layout of the two probe wires leading to the measuring
instrument became hopelessly involved in the measurement. The same sort of uncertainty arises if we take Faraday’s Law of Induction http://www.ivorcatt.uk/images/7877.jpg
, or the Biot-Savart
law (or Ampere’s Rule) and try to apply it to a TEM wave travelling at the
speed of light. It is necessary to think clearly about the physics involved,
and not just hope the maths will sort itself out on its own. Ivor
Catt 18june02 (Tolly = Dr. Anatol Holt) |

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