You are given a parallel-plate capacitor that consists of a thick dielectric layer (e) bounded by...

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You are given a parallel-plate capacitor that consists of a thick dielectric layer (e) bounded by metal plates. A cylindrical metal bar of radius o is placed at the exact center of the dielectric layer along the x axis, as shown in the illustration below. The metal bar is biased at V = 0, while the potential difference between the metal plates is Vo. The separation between the metal plates d' is much larger than the bar, i.e., d>> ô. E & 2 (1) What is the electric field near the metal plates? (2) Find the boundary condition(s) that should be satisfied by the potential distribution in the dielectric layer. (3) Find the potential distribution. (4) Find the electric field, flux density, and polarization distribution along the dashed line. The dashed line cross the center of the cylinder along the x axis. What is the highest electric field in the system? (5) Compare the potential and electric field distribution for the capacitors with and without the metal bar. (6) Compare the capacitance for the capacitors with and without the metal bar. You are given a parallel-plate capacitor that consists of a thick dielectric layer (e) bounded by metal plates. A cylindrical metal bar of radius o is placed at the exact center of the dielectric layer along the x axis, as shown in the illustration below. The metal bar is biased at V = 0, while the potential difference between the metal plates is Vo. The separation between the metal plates d' is much larger than the bar, i.e., d>> ô. E & 2 (1) What is the electric field near the metal plates? (2) Find the boundary condition(s) that should be satisfied by the potential distribution in the dielectric layer. (3) Find the potential distribution. (4) Find the electric field, flux density, and polarization distribution along the dashed line. The dashed line cross the center of the cylinder along the x axis. What is the highest electric field in the system? (5) Compare the potential and electric field distribution for the capacitors with and without the metal bar. (6) Compare the capacitance for the capacitors with and without the metal bar.