Q3. Observation Point y Figure 2. The geometry of the problem 3 In Figure 2, the constant charge density distribution po (C/m²) is defined on the surface located at x-y plane. In the question, the parts of a ring are given. Here, a is the inner radius and b is the outer radius. Dielectric permittivity of the space is €. Hint: The ring pieces are located at x-y plane and each of them is scanning 200 angle in the space. a) Find the electric field at an any point located at (0,0,z). Do not forget that Electric Field is a vector.) b) By taking the limit cases, find the electric field at the same point (0,0,z) for the following figures. In the following figures, the top views are given. No need to show all steps, just give the final answers. Hint: No need to do everything from beginning. Just try to take the limits or change the boundaries of the integral. c) Verify the last figure (Infinite Sheet) with Gauss' Law. i. ii. iii. iv. Ring Shape Disk Shape Bow - Tie Shape Infinite Sheet b 200
Observation Point Figure 2. The geometry of the problem 3 In Figure 2, the constant charge density distribution po (C/m²) is defined on the surface located at x – y plane. In the question, the parts of a ring are given. Here, a is the inner radius and b is the outer radius. Dielectric permittivity of the space is eg. Hint: The ring pieces are located at x - y plane and each of them is scanning 20, angle in the space. a) Find the electric field at an any point located at (0,0,z). Do not forget that Electric Field is a vector.) b) By taking the limit cases, find the electric field at the same point (0,0,z) for the following figures. In the following figures, the top views are given. No need to show all steps, just give the final answers. Hint: No need to do everything from beginning. Just try to take the limits or change the boundaries of the integral. c) Verify the last figure (Infinite Sheet) with Gauss' Law. i. Ring Shape iii. Bow - Tie Shape ii. iv. Disk Shape Infinite Sheet b 200
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