96 Capacitance and DielectricsP26.58(a)We use Equation 26.11 to find the potential energy of the capacitor. As we will see, thepotential difference ∆Vchanges as the dielectric is withdrawn. The initial and finalenergies are UQCii=FHGIKJ122andUQCff=FHGIKJ122.But the initial capacitance (with the dielectric) is CCif=κ. Therefore, UQCfi=FHGIKJ122κ.Since the work done by the external force in removing the dielectric equals the change inpotential energy, we have WUUQCQCQCfiiii=−=FHGIKJ−FHGIKJ=FHGIKJ−1212121222κκaf.To express this relation in terms of potential difference ∆Vi, we substitute QCVii=∆bg, andevaluate: WCVii=−=×−=×−−121122 00101005 001 004 00102925∆bg afejaf afκ....FVJ.The positive result confirms that the final energy of the capacitor is greater than the initialenergy. The extra energy comes from the work done on
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