Q3S - charge Q 1 in the half without the slab, and Q 2 in...

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Quiz 3 Solutions Check the best answer. 1. A small electric dipole p is in a feld E . Which oF these is wrong? IF p E there is no torque on the dipole. IF E is uniForm, there is no net Force on the dipole. Stable equilibrium occurs iF p is directed opposite to a uniForm E . [Unstable with respect to rotation.] IF E is not uniForm and p E , there is a net Force on the dipole toward the region oF stronger E . Check T or ± depending on whether the statement is true or False. 2. Two capacitors connected in parallel have larger total capacitance than iF they are connected in series. T ± Physics 54 Summer 2011 1

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3. An isolated parallel plate capacitor with charge Q has a slab of dielectric Flling half of the space between the plates as shown. The plates have area A and are separated by distance d . The slab has dielectric constant κ . a. Consider the two halves of the region between the plates. The potential difference between the plates is Δ V in both, so the total E-Feld between the plates is the same in both. This means the charges on the plates are not the same in both halves. ±ind the
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Unformatted text preview: charge Q 1 in the half without the slab, and Q 2 in the half with the slab, in terms of Q and . [±irst Fnd the charge densities σ 1 and 2 .] b. ±ind Δ V in terms of Q , and Fnd the capacitance of the system. c. In which half of the capacitor is the energy density larger? How do you know? a. On the half of the plate above the empty gap the charge density is 1 where E = 1 / ε . On the half above the slab the charge density is 2 , where E = 2 / κε . Thus 2 = κσ 1 and Q 2 = Q 1 . Since Q 1 + Q 2 = Q we Fnd Q 1 = Q 1 + and Q 2 = Q 1 + . b. Since Δ V = Ed and E = Q 1 ⋅ ( A /2) = 2 Q A ⋅ 1 1 + , we have Δ V = 2 d A ⋅ 1 1 + ⋅ Q . Using C = Q / Δ V we Fnd C = 1 + 2 ⋅ A d . c. The energy density is give by u e = 1 2 E 2 . Since E is the same in both halves, u e is larger in the half with the slab. + Q − Q Physics 54 Summer 2011 2...
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This note was uploaded on 10/19/2011 for the course PHYSICS 54L taught by Professor Thomas during the Summer '09 term at Duke.

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Q3S - charge Q 1 in the half without the slab, and Q 2 in...

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