Solucionario

CHAPTER 24: Capacitance, Dielectrics, Electric Energy Storage Responses to Questions
1. Yes. If the conductors have different shapes, then even if they have the same charge, they will have different charge densities and therefore different electric fields near the surface. There can be a potential difference between them. The definition of capacitance C = Q/V cannot be used here because it isdefined for the case where the charges on the two conductors of the capacitor are equal and opposite. Underestimate. If the separation between the plates is not very small compared to the plate size, then fringing cannot be ignored and the electric field (for a given charge) will actually be smaller. The capacitance is inversely proportional to potential and, for parallel plates, also inverselyproportional to the field, so the capacitance will actually be larger than that given by the formula. Ignoring fringing field effects, the capacitance would decrease by a factor of 2, since the area of overlap decreases by a factor of 2. (Fringing effects might actually be noticeable in this configuration.) When a capacitor is first connected to a battery, charge flows to one plate. Because the platesare separated by an insulating material, charge cannot cross the gap. An equal amount of charge is therefore repelled from the opposite plate, leaving it with a charge that is equal and opposite to the charge on the first plate. The two conductors of a capacitor will have equal and opposite charges even if they have different sizes or shapes. Charge a parallel-plate capacitor using a battery witha known voltage V. Let the capacitor discharge through a resistor with a known resistance R and measure the time constant. This will allow calculation of the capacitance C. Then use C = ε0A/d and solve for ε0. Parallel. The equivalent capacitance of the three capacitors in parallel will be greater than that of the same three capacitors in series, and therefore they will store more energy whenconnected to a given potential difference if they are in parallel. If a large copper sheet of thickness l is inserted between the plates of a parallel-plate capacitor, the charge on the capacitor will appear on the large flat surfaces of the copper sheet, with the negative side of the copper facing the positive side of the capacitor. This arrangement can be considered to be two capacitors in series,each with a thickness of 1  d  l  . The new net capacitance will be 2

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C    0 A  d  l  , so the capacitance of the capacitor will be reduced.

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A force is required to increase the separation of the plates of an isolated capacitor because you are pulling a positive plate away from a negative plate. The work done in increasing the separation goesinto increasing the electric potential energy stored between the plates. The capacitance decreases, and the potential between the plates increases since the charge has to remain the same. (a) The energy stored quadruples since the potential difference across the plates doubles and the capacitance doesn’t change: U  1 CV 2 . 2 (b) The energy stored quadruples since the charge doubles and thecapacitance doesn’t change: Q2 U1 . 2 C
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Chapter 24

Capacitance, Dielectrics, Electric Energy Storage(c) If the separation between the plates doubles, the capacitance is halved. The potential difference across the plates doesn’t change if the capacitor remains connected to the battery, so the energy stored is also halved: U  1 CV 2 . 2 10. (c) If the voltage across a capacitor is doubled, the amount of energy it can store is quadrupled: U  1 CV 2 . 2 11. The dielectric will be pulled into...