D3.1. Given a 60-μC point charge located at the origin, find the total electric flux passing through: (a) that portion of the sphere r = 26 cm bounded by 0 <0<л/2 and 0 <<л/2; (b) the closed surface defined by p = 26 cm and z = +26 cm; (c) the plane z = 26 cm.

A solid conducting sphere of radius R carries a charge +Q. A thick conducting shell is concentric with the sphere and has an inner radius R2 and outer radius R3. The shell carries a charge -Q. The figure shows a cross section. a) Where are the charges located? Add charge symbols to the figure. R1 R3 R2 b) Add a few electric field lines and equipotential lines to the figure. Please label the lines clearly. c) Draw a sketch of the potential as a function of distance from the center of the sphere. Please label all interesting points on the graph.

2) If the angle the displacement makes with the electric field is 0° it means the charge is moving along (or parallel to) the field vectors. Is work being done? How will the angle here affect the work done, explain your answer with a diagram? Last Revised 12/21/2015 Equipotential Surfaces – 3.1

Two infinitely long, parallel lines of charge with linear charge densities 9.0 µC/m and −9.0 µC/m are separated by a distance of 0.50 m. What is the net electric field at point C as shown in the figure below? (Express your answers in vector form.)