Simple Nature - Light and Matter

Discussion QuestionsA The figure shows a positive charge in the gap between two capacitorplates. Compare the energy of the electric fields in the two cases. Doesthis agree with what you would have expected based on your knowledgeof electrical forces?B The figure shows a spherical capacitor. In the text, the energy storedin its electric field is shown to be(U e = kq2 12 a − 1 ).bd / Discussion question A.What happens if the difference between b and a is very small? Does thismake sense in terms of the mechanical work needed in order to separatethe charges? Does it make sense in terms of the energy stored in theelectric field? Should these two energies be added together?Similarly, discuss the cases of b → ∞ and a → 0.C Criticize the following statement: “A solenoid makes a charge in thespace surrounding it, which dissipates when you release the energy.”D In example 16 on page 585, I argued that for the charges shownin the figure, the fields contain less energy when the charges are closertogether, because the region of cancellation expanded, while the regionof reinforcing fields shrank. Perhaps a simpler approach is to considerthe two extreme possibilities: the case where the charges are infinitelyfar apart, and the one in which they are at zero distance from each other,i.e., right on top of each other. Carry out this reasoning for the case of(1) a positive charge and a negative charge of equal magnitude, (2) twopositive charges of equal magnitude, (3) the gravitational energy of twoequal masses.e / Discussion question B.10.4.2 Gravitational field energyExample B depended on the close analogy between electric andgravitational forces. In fact, every argument, proof, and examplediscussed so far in this section is equally valid as a gravitationalexample, provided we take into account one fact: only positive massexists, and the gravitational force between two masses is attractive.This is the opposite of what happens with electrical forces, whichare repulsive in the case of two positive charges. As a consequence ofthis, we need to assign a negative energy density to the gravitationalfield! For a gravitational field, we havedU g = − 18πG g2 dv ,where g 2 = g · g is the square of the magnitude of the gravitationalfield.10.4.3 Magnetic field energySo far we’ve only touched in passing on the topic of magneticfields, which will deal with in detail in chapter 11. Magnetism isan interaction between moving charge and moving charge, i.e., betweencurrents and currents. Since a current has a direction inSection 10.4 Energy In Fields 587