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I was thinking about this more, and there is unfortunately the idea of matching the resistor to the impedance of the line is going to fail badly. The idea works when the resistor is at the end of the transmission line, terminating it - but if it's sliding along the line, the resistor will be in parallel with the rest of the line, creating a mismatch. I am thinking now that what is needed in an attempt to save the approach is to make the resistance "high". Then we ignore the disturbing effect the resistor has on the line. Unfortunately, that loses the idea of the generator power all flowing through the line to the resistor :(.
We can also just try dealing with the reflections in the line, I suppose. But I think these problems illustrate how the idea of a "wire" is idealized and also non-relativistic - it conducts energy with infinite speed and you don't have to worry about effects like capacitance and inductance. The real word equivalent is going to exhibit much more complex behaviors, consistent with the idea that energy propagates through fields that propagate (in a vacuum) at the speed of light.
We can also just try dealing with the reflections in the line, I suppose. But I think these problems illustrate how the idea of a "wire" is idealized and also non-relativistic - it conducts energy with infinite speed and you don't have to worry about effects like capacitance and inductance. The real word equivalent is going to exhibit much more complex behaviors, consistent with the idea that energy propagates through fields that propagate (in a vacuum) at the speed of light.
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