47. Assuming the charge on one plate is +qand the charge on the other plate is−q, we fnd an expression Forthe electric feld in each region, in terms oFq, then use the result to fnd an expression For the potentialdi±erenceVbetween the plates. The capacitance isC=qV.The electric feld in the dielectric isEd=q/κε0A,whereκis the dielectric constant andAis the platearea. Outside the dielectric (but still between the capacitor plates) the feld isE=q/ε0A. The feld isuniForm in each region so the potential di±erence across the plates isV=Edb+E(d−b)=qbκε0A+q(d−b)ε0A=qε0Ab+κ(d−b)κ.The capacitance isC=qV=κε0Aκ(d−b)+b=κε0Aκd−b(κ−1).The result does not depend on where the dielectric is located between the plates; it might be touchingone plate or it might have a vacuum gap on each side.²or the capacitor oF Sample Problem 26-8,
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.