EM Waves & Conservation of Energy

Hello folks. This is Sandeep. I have many lingering doubts in physics that I am here to get cleared. This has become more of an issue ever since I decided to teach physics to my young nephew.

My first question pertains to electromagnetic waves and the conservation of energy.

Consider an AC circuit. It's power consumption P1 is the heat loss from resistance. The circuit will have an electrical and magnetic field associated with it. Let us now introduce a coil in the electrical and magnetic field of our circuit. We know that an electric current will be induced in the coil. There will be some power consumption in the coil, in the form of heat loss, due to the resistance of the coil. Let us call it P2.

My question is this: What is the source of the power P2? It may be argued that the coil will have to have its own power source, but there are some crystal receivers, which do not have their own power source.

Staff Emeritus
2021 Award
It's power consumption P1 is the heat loss from resistance

No, it's power loss is the sum of heat loss through resistance plus the energy radiated away in radio.

jtbell
Mentor
And part of the energy that is radiated away from the AC circuit via radio waves, becomes electrical energy in the coil, which ends up as... (you can complete this sentence). An ideal inductor (which does not exist in nature) does not dissipate any real power. It stores reactive power. Heat dissipation in electrical components is like heat dissipation by friction in mechanical components. The power dissipated by heat has to come from somewhere though. The components of a circuit that have no power source will not dissipate any power (aside from background noise and/or incident radiation). An inductor is like a flywheel; it is an energy storing device. Energy is stored in the inductor's magnetic field. The energy stored in an inductor is proportional to the square of the current through the inductor.

Similarly, ideal capacitors (which do not exist in nature) do not dissipate any real power. They store reactive power. Energy is stored in the capacitor's electric field. The energy stored in a capacitor is proportional to the square of the voltage across the capacitor.

Duality is cool.

Please correct me if I am wrong, but perhaps the explanation on why I did not read about EM radiation loss in my physics textbook is because EM radiation becomes an issue only if the size of the circuit is comparable to the wavelength of the AC signal driving it (http://physics.stackexchange.com/qu...ttle-questions-about-radiation-of-lc-circuits). Unless we are dealing with very high frequencies, this wavelength is much much much larger than the size of the circuit, so this loss is truly negligible. Is this correct?

Also, could you kindly confirm my understanding that a DC will experience EM loss only during the transient phase?

nsaspook
Please correct me if I am wrong, but perhaps the explanation on why I did not read about EM radiation loss in my physics textbook is because EM radiation becomes an issue only if the size of the circuit is comparable to the wavelength of the AC signal driving it (http://physics.stackexchange.com/qu...ttle-questions-about-radiation-of-lc-circuits). Unless we are dealing with very high frequencies, this wavelength is much much much larger than the size of the circuit, so this loss is truly negligible. Is this correct?

The size is the 'electrical' size of the circuit. This might be much smaller than the physical size of components. So if the electrical length is a small fraction, loss from EM radiation will usually be small in a circuit not designed to be an antenna.
http://en.wikipedia.org/wiki/Electrical_length

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For low frequency circuits (so called "lump circuits"), electrical length is so small that it is completely neglected. When you start dealing with RF/microwave circuits, transmission lines, and antennas, then you have to take electrical length into consideration.

For lumped circuit analysis, just remember V = IR, Kirchoff's Current Law (KCL), Kirchoff's Voltage Law (KVL), i = c dv/dt (current through a capacitor), and v = L di/dt (voltage across an inductor). For sinusoidal, steady-state stuff, remember that ZL = j*omega*L, Zc = 1/(j*omega*C), and omega = 2*pi*f. Also, for sinusoidal, steady-state stuff, the power analysis can be tricky. That is, you have complex power (real dissipated power and imaginary reactive power), and leading / lagging power factors.

A good text book on circuit analysis is the one by Hayt and Kemmerly: "Engineering Circuit Analysis."

nsaspook