914_Physics ProblemsTechnical Physics

914_Physics ProblemsTechnical Physics - 254 Inductance...

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254 Inductance Additional Problems *P32.59 (a) Let Q represent the magnitude of the opposite charges on the plates of a parallel plate capacitor, the two plates having area A and separation d . The negative plate creates electric field E = Q A 2 0 toward itself. It exerts on the positive plate force F = Q A 2 0 2 toward the negative plate. The total field between the plates is Q A 0 . The energy density is u E Q A Q A E = = = 1 2 1 2 2 0 2 0 2 0 2 2 2 0 2 . Modeling this as a negative or inward pressure, we have for the force on one plate F PA Q A = = 2 0 2 2 , in agreement with our first analysis. (b) The lower of the two current sheets shown creates above it magnetic field B k = µ 0 2 J s ± e j . Let A and w represent the length and width of each sheet. The upper sheet carries current J w s and feels force F B i k j = × = × − = I J w J w J s s s A A A µ µ 0 0 2 2 2 ± ± ± e j . The force per area is P F w J s = = A µ 0 2 2 . y x z J s J s FIG. P32.59(b) (c) Between the two sheets the total magnetic field is
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