PES 1120: Homework assignment 2 [24 points] Handed out: Friday February 7 Due in: Wednesday February 12, at the start of class 6:05pm Worth 3% of your total grade. Show all reasoning and workings. Part 1: fully graded questions [18 points] Question 1 [12 points] Negative charge -Q is distributed uniformly around a quarter-circle of radius R that lies in the first quadrant, with the center of curvature at the origin. a)[1 point] In which direction does the electric field point at the origin, which is marked with O on the diagram? Explain your reasoning. b)[1 point] Add variables to your diagram that can be used to construct an integral to add the fields caused by each little section of charge dq. c)[1 point] Write an expression for the electric charge dq in terms of dθ (use s = Rθ) in that short section of the charge distribution. d)[3 points] Write expressions for the non-zero components (both x- and y-components) of the electric field at O caused by the designated charge dq in part b). e)[3.5 points] Write the integral with the appropriate limits and complete the integral. Show that you get get E x = E y = Q/(2π 2 0 R 2 ). f)[1.5 points] Find an algebraic expression for the magnitude and direction of the electric field at the origin. For the direction of the electric field compare your result to your answer in part a). g)[1 point]If R →∞, what is the limit of the expression for the electric field found in part f)? Why does this make sense? Hint: This question is similar to the worked sample problem on p.588-589 of the 9th edition and on p.641-642 of the 10th edition of your textbook.