Question

Mechanics

3.1. Consider the capacitor in Problem 2, and describe how the capacitor contains energy inside of it. Describe this energy in two different ways, the first using the capacitor geometry properties, and the second, in terms of the fundamental electric field strength contained inside the volume of the capacitor. Is the form of this energy constant in time, or does it change over time into a different form of energy? Draw a diagram, and show that these two perspectives of circuit analysis and fundamental fields are the same! (hint: go back and explain where the electric field comes from inside an ideal parallel plate capacitor).

3.2. Consider the inductor in Problem 2, and describe how the inductor contains energy inside of it. Describe this energy in two different ways, the first using the inductor geometry properties, and the second, in terms of the fundamental magnetic field strength contained inside the volume of the inductor. Is the form of this energy constant in time, or does it change over time into a different form of energy? Draw a diagram, and show that these two perspectives of circuit analysis and fundamental fields are the same! (hint: go back and explain where the magnetic field comes from inside an ideal solenoid).

3.3. Consider the electromagnetic radiation in Problem 1. Describe the energy contained inside the EM wave.Is the energy constant in time or changing in time? Where does this energy come from? Explain the concept of energy density, and how it can be used to find the total energy in a certain region of space. How does the PoyntingVector relate to this energy? Draw a diagram and explain also explain your reasoning with words.