P26_041 - C eq oF two capacitors in series, one with...

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41. We assume there is charge q on one plate and charge q on the other. The electric feld in the lower halF oF the region between the plates is E 1 = q κ 1 ε 0 A , where A is the plate area. The electric feld in the upper halF is E 2 = q κ 2 ε 0 A . Let d/ 2 be the thickness oF each dielectric. Since the feld is uniForm in each region, the potential di±erence between the plates is V = E 1 d 2 + E 2 d 2 = qd 2 ε 0 A · 1 κ 1 + 1 κ 2 ¸ = qd 2 ε 0 A κ 1 + κ 2 κ 1 κ 2 , so C = q V = 2 ε 0 A d κ 1 κ 2 κ 1 + κ 2 . This expression is exactly the same as the that For
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Unformatted text preview: C eq oF two capacitors in series, one with dielectric constant 1 and the other with dielectric constant 2 . Each has plate area A and plate separation d/ 2. Also we note that iF 1 = 2 , the expression reduces to C = 1 A/d , the correct result For a parallel-plate capacitor with plate area A , plate separation d , and dielectric constant 1 ....
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