3. [8pts] Derive an expression for the electric field dỄ of the infinitesimal piece at the observation location. Express your result in terms of the given variables and known constants. 4. [8pts] Integrate over the charge distribution to determine the net electric field Ẽ at the origin. Your answer should only contain the given variables and known constants. 5. [8pts] What does your result from part 4 say about the cases where (i) the bent rod is a half-circle (a = π): - What is the net field E at the origin in this case? - What consequence does the mirror symmetry of the half-circle have for the net field Ē at the origin? (ii) the bent rod forms a complete circle (a = 2π): Show that your result for the net field Ę in the center of this circular rod is consistent with our formula for the field of a ring. A thin plastic rod is bent into a circular arc of radius R, angle a, and with center at the origin as indicated in the diagram. The rod carries a uniformly distributed charge q and is located in the x-y-plane. Answer the following questions to determine the electric field at the origin. de 1. [5pts] Consider an infinitesimal piece of the bent rod with angular length de, located at an angle 0 from the +y axis as shown in the schematic. Find an expression for the relative position vector that points from the center of this infinitesimal piece to the observation location at the origin. 2. [5pts] Determine an expression for the charge dq on the infinitesimal piece of rod in terms of de and relevant known variables.