PHYS 143 Fall 24 Turn-In 3 PDF

PHYS 143 Turn-In 3 FALL 24 Please complete the following two questions. Remember that your answer should be detailed and be presented in...

PHYS 143 Turn-In 3 FALL 24 Please complete the following two questions. Remember that your answer should be detailed and be presented in textbook style with steps, explanations, and diagrams. Be sure to consult the turn-in problem guidelines on the canvas page. Problem 1: (Charged Arcs) Two uniformly charged circular arcs of radius R and line charge λ lie on the first and third quadrants on the xy-plane (see figure below). Each arc spans an angle of π/3. Consider the point P directly above the center of the charge distribution on the z-axis. (a) Which components of the electric field at P are zero, if any? Use symmetry to support your answer. (b) Calculate the magnitude and direction of the electric field at point P. (Hint: The length of an arc of angle θ and radius r is s = rθ) Problem 2: (Gauss’s without Gauss’s) You have a point with charge q at the origin and surround the charge with a cube as a Gaussian surface. (a) Try (but don’t actually calculate! ) the electric flux due to the charge using the cube. Explain why this would be so difficult to do. (b) Instead, use a sphere as the Gaussian surface and actually compute the electric flux. 1