P26_047 - 47. Assuming the charge on one plate is +q and...

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47. Assuming the charge on one plate is + q and the charge on the other plate is q , we fnd an expression For the electric feld in each region, in terms oF q , then use the result to fnd an expression For the potential di±erence V between the plates. The capacitance is C = q V . The electric feld in the dielectric is E d = q/κε 0 A ,where κ is the dielectric constant and A is the plate area. Outside the dielectric (but still between the capacitor plates) the feld is E = q/ε 0 A . The feld is uniForm in each region so the potential di±erence across the plates is V = E d b + E ( d b )= qb κε 0 A + q ( d b ) ε 0 A = q ε 0 A b + κ ( d b ) κ . The capacitance is C = q V = κε 0 A κ ( d b )+ b = κε 0 A κd b ( κ 1) . The result does not depend on where the dielectric is located between the plates; it might be touching one 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.

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