# hw04 - ± Q is put on the plates The space between the...

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Homework for week 4 Due Thu, 2/25 (in class) Instructions: Please explain your reasoning in detail. State where the formulas are coming from, and why they are applicable here. (The goal is, after all, that we can check and possibly correct your way of thinking.) Please write legibly, and draw large and clearly labeled sketches. 5. A capacitor network consisting of three identical capacitors with the capacitance C is shown on the figure. (a) When an ideal battery with voltage V is connected to this network, what are the charges q 1 , q 2 and q 3 , on all three capacitors? (b) What happens to the charges on the three capacitors if a wire is connected between points A and B? 6. A capacitor with horizontal plates of area A and separation d is in a homogeneous vertical gravitational field. The volume of the capacitor initially empty – the space between the plates is filled with air. A constant charge

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Unformatted text preview: ± Q is put on the plates. The space between the plates is gradually being ﬁlled with water with dielectric con-stant κ . At any instant the height ﬁlled with water is h (where 0 < h < d ). (a) What is the initial capacitance (for h = 0)? (b) What is the initial voltage? (c) What is the initial energy stored in this capacitor? (d) For h = d/ 2, graph the magnitude of the electric ﬁeld E , as a function of the distance from the bottom plate, h . (e) Discuss where free and induced charged densities are located and how they relate to the graph from part (d). 1 (f) For for h = d/ 2, sketch the potential as a function of z . (g) Calculate the capacitance as a function of h . (h) Calculate the energy stored in the capacitor as a function of h . 2...
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