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 As we will see, thepotential difference ∆Vchanges as the dielectric is withdrawn.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=FHGIKJ122.Since the work done by the external force in removing the dielectric equals the change inpotential energy, we have WU UQCQCQCfiiii=−=FHGIKJ−FHGIKJ=FHGIKJ−1212121222κκaf.To express this relation in terms of potential difference ∆Vi, we substitute QC Vii=∆bg, andevaluate: WCV=×−=×−−12112200 10100500 100400 102925∆afejafaf....F VJ.The positive result confirms that the final energy of the capacitor is greater than the initialenergy. The extra energy comes from the work done onthe system by the external force thatpulled out the dielectric.
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .