Problem 4 It points possible [graded] 0'0 Consider a thin plastic rod bent into a semicircular arc of radius R with center at the origin as shown in the figure. The rod carries a unformly distributed positive charge +Q. Let a point 17" on the arc be specified by an angle 9, where 9 is measured from the positive 3; axis and increases in the counterclockwise direction. Throughout this problem, use I: for Coulomb's constant. Determine the electric field dE at the origin due to the indicated infinitesimal piece of the rod at an angle I9, that subtends an angle A6. Express your answer in terms of 6', AB, R, Q and fundamental constants. are... [1E2 = Calculate the electric field E at the origin due to the entire semicircular rod. Your answer should be a vector. E. _ Now consider an additional thin plastic rod bent into a semicircular arc of radius R with center at the origin as shown in the diagram. This rod carries a uniformly distributed negative charge Q. Together, these bet rods form a perfect circle. What is the direction of the electric field at location > R? Hint: consider how this object would appear from far away. 0 +33, because the ring looks like a :'i': dipole from far away. O r', because the ring looks like a +55: dipole from far away. 0 There is no electric fieldr because the ring looks like a point charge with Qnet = 0 from far away