Answer Happy

1. (a) 1 point Consider an infinitely long wire with uniform charge density i per unit length. What can you say about the electric field around the wire based on the symmetry of the problem alone? [This is a conceptual question: think about the problem as stated. We are not asking what the electric field is, but what you can say about it based on the symmetry of the problem. (b) 2 points Based on only the above symmetry considerations calculate from first prin- ciples (without using Gauss' law) the total flux fĒ dĀ through the surface area of a cylinder of radius r and length I centred around a section of the above wire, see diagram below? [Hint: Your answer will be in terms of the unknown strength of the electric field E(r) at a distance r from the wire.] (c) 2 points Use Gauss' law to relate the charge density 2 to the total flux $ dĀ through the surface area of the above cylinder. (a) I point combine the previous two answers to determine the strength of the electric field E(r) at a distance r away from the wire. (e) 2 points Consider a straight wire of finite length with a uniform charge density. De- scribe the region in which we can approximately determine the electric field around the wire by treating it as infinitely long and apply the result for E(r) you just derived? (1) 2 points Consider the above 100 m long wire carrying a net charge of 1 uc. What is the magnitude of the electric force acting on a proton 0.1 m away from the above wire around the middle region 50 m from the end points. What is the direction of the force?