Turn-in HW 3: Electric Field of Continuous Charge Distribution HW A plastic rod, shown at right, has a negative, uniform linear y charge density .1 = I.iol and is bent into a quarter circle (radius R) situated as shown. Your goal is to find the electric field at the origin. Express all of your answers in I ' terms of given quanties and constants. I 1. What is the total charge on the quarter circle? 2. Label a generic small chunk of charge dq at an angle 6 as shown in the gure. Draw a vector, at the origin, representing the field at the origin due to that small piece of charge. 3. Determine expressions for: a. The magnitude of the electric field at the origin due to your chosen small chunk of charge. b. The x- and 1 - components of the electric field at the origin due to your chosen small chunk of charge. 4. Express, but do not evaluate, definite integrals for the x- and 3; components of the net electric field at the origin. 5. Evaluate the integrals and write the net electric field in component form. In which direction does the electric field point? Does your result make sense? Explain why or why not. 6. Now we'll redo the problem with a varying charge density given by 1(9) = |.io|cos(l9). (Note: Use the angle 8 as shown, where 9 = {J is along the -x axis). What is the total charge on this quarter circle? (You might be well served by considering Eqns. 23.15/16.) Does it make sense compared to the uniform charge density case you did above? 7. Again, write the net electric field in component form. In which direction does the electric field point? How does it compare to the constant density case above? Does your result make sense? Explain why or why not