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# written14 - Homework 14 Due 1 A L L square slab with...

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Homework 14 Due April 24 2007 1) A LL × square slab with thickness d of dielectric with dielectric constant κ is partially inserted a distance x between the plates of a parallel plate capacitor as shown below. The plates are also squares of dimension × and are separated by a distance dL ± . (a) If the capacitor is connected to a battery with emf 0 V , what is the charge stored in this capacitor as a function of x ? (b) In the situation of part (a), what is the electric potential energy stored in this capacitor as a function of x ? (c) In the situation of part (a), if the dielectric is moving in the x-direction at a velocity v, what is the current flowing through the wire at point P? (d) In the situation of part (a), how much work does the battery do when the slab is moved from the position x =0 to x = L ? Show that this is twice the change in the stored energy of the capacitor as the slab moves from x =0 to x = L . (e) Explain how the result in part (d) is consistent with the law of conservation of energy. In particular explain why this implies that a force is exerted on the slab. Which direction is the force? (f) Now consider the slightly different situation where the same capacitor is disconnect but has a charge 0 Q stored on the plates. What is the potential difference between the plates as a function of x ? (g) In the situation of part (f), what is the electric potential energy stored in the capacitor as a function of the position x ?

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written14 - Homework 14 Due 1 A L L square slab with...

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