4321_HW10FA08 - Physics 4321 Homework Set 10 Due z 1 A...

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Physics 4321 Homework Set 10 November 10, 2008 Due: November 17, 2008 1. A permanently polarized slab has lateral dimensions much larger than its thickness. Its polarization is P = P o z ^ and its thickness is a. It is placed between two conducting plates that are connected by a conducting wire; i.e.; the plates are shorted. The distance between the conducting plates is a + b. (a) Calculate the electric field and the electric displacement inside the dielectric, inside the plates above the dielectric, and outside the plates. (b) Calculate the bound surface charge density on the dielectric. (c) Calculate the free surface charge density on each conducting plate. Hint: Note that V between the plates must be zero since they are shorted. 2. A wire having length 2 a and carrying current I lies along the x axis as shown. (a) Starting with the Biot-Savart law, calculate the magnetic field B in the x-y plane at the point x = 2 a , y = a . (b) What is the field at x = 2 a , y = 0? 3. Use Ampere's Law to calculate the magnetic field due to the
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