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c0 qd v 0 a physics 2b summer

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Unformatted text preview: lmer August 19, 2013 b - - - - - - - - - - + + + + + + + + + + 21 ε 0 Φ E = ε 0 κ E ⋅ dA = QFree, Enclosed ∫   This capacitor is filled in part by a dielectric with thickness b<d.   What is the electric field inside the capacitor but outside the dielectric? A) B) Q Q E= E= ˆ y ε 0κ A C) Q ˆ E=− y ε 0κ A D) ˆ y ε0 A Q ˆ E=− y ε0 A Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 b - - - - - - - - - - + + + + + + + + + + 22 ε 0 Φ E = ε 0 κ E ⋅ dA = QFree, Enclosed ∫   This capacitor is filled in part by a dielectric with thickness b<d. ⎧Q ˆ y Outside Dielectric ⎪ε0 A ⎪ E=⎨ ⎪ Q y Inside Dielectric ˆ ⎪ ε 0κ A ⎩ Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 b - - - - - - - - - - + + + + + + + + + + 23   This capacitor is filled in part by a dielectric with thickness b<d. ⎧Q ˆ Outside Dielectric ⎪ε A y ⎪0 E=⎨ ⎪ Q y Inside Dielectric ˆ ⎪ ε 0κ A ⎩ ΔV = − ∫ + − E ⋅ ds Q Q = b+ ( d − b) ε 0κ A ε0 A Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 b - - - - - - - - - - + + + + + + + + + + 24   This capacitor is filled in part by a dielectric with thickness b<d. Q Q ΔV = b+ ( d − b) ε 0κ A ε0 A 1 ΔV = CQ b ⎞ 1⎛ Q Q =⎜ b+ ( d − b)⎟ Q ⎝ κε 0 A ε0 A ⎠ ⎛b ( d − b) ⎞ =⎜ + κε A εA ⎟ ⎝ ⎠ 0 0 Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 - - - - - - - - - - + + + + + + + + + + 25   This capacitor is filled in part by a dielectric with thickness b<d. 1 b ( d − b) = + C κε 0 A ε0 A b   Note this is the same as adding two capacitors in series!   One with dielectric, κ, and thickness b   Another without any dielectric and thickness d–b Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 - - - - - - - - - - + + + + + + + + + + 26   Think about what is different when you have two capacitors with…   Identical geometry   Different dielectrics inside   Same voltage applied   Be able to…   Find the total capacitance   Find the energy stored on each   Find the charge stored on each Physics 2B - Summer Session 2 - C. Palmer August 19, 2013 27 Physics Concept Circuits Components Learning Outcome Direct Current Alternating Current Impedance Evaluate problems with resistors, capacitors, and batteries (DC) in parallel and series. Explain beh...
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