Simple Nature - Light and Matter

for the purposes of this problem, assume that they still have approximatelythe kind of idealized field pattern shown in the figure.Each capacitor has an interior volume of 1.00 m 3 , and is charged upto the point where its internal field is 1.00 V/m.(a) Calculate the energy stored in the electric field of each capacitor√when they are separate.(b) Calculate the magnitude of the interior field when the two capacitorsare put together in the manner shown. Ignore effects arisingfrom the redistribution of each capacitor’s charge under the influenceof the other capacitor.√(c) Calculate the energy of the put-together configuration. Does assemblingthem like this release energy, consume energy, or neither?√28 Find the capacitance of the surface of the earth, assumingthere is an outer spherical “plate” at infinity. (In reality, this outerplate would just represent some distant part of the universe to whichwe carried away some of the earth’s charge in order to charge up the√earth.)29 (a) Show that the field found in example 10 on page 574reduces to E = 2kλ/R in the limit of L → ∞.(b) An infinite strip of width b has a surface charge density σ. Findthe field at a point at a distance z from the strip, lying in the plane√perpendicularly bisecting the strip.(c) Show that this expression has the correct behavior in the limitwhere z approaches zero, and also in the limit of z ≫ b. For thelatter, you’ll need the result of problem 22a, which is given on page930.30 A solid cylinder of radius b and length l is uniformly chargedwith a total charge Q. Find the electric field at a point at the centerof one of the flat ends.31 Find the voltage at the edge of a uniformly charged disk.(Define V = 0 to be infinitely far from the disk.)√⊲ Hint, p. 920Problem 29.32 Find the energy stored in a capacitor in terms of its capacitanceand the voltage difference across√it.33 (a) Find the capacitance of two identical capacitors in series.(b) Based on this, how would you expect the capacitance of aparallel-plate capacitor to depend on the distance between the plates?34 (a) Use complex number techniques to rewrite the function√f(t) = 4 sin ωt + 3 cos ωt in the form A sin(ωt + δ).(b) Verify the result using the trigonometric identity sin(α + β) =sin α cos β + sin β cos α.35 (a) Show that the equation V L = L dI/ dt has the rightProblems 639