Question

Constants Periodic Table Part A A thin rod bent into the shape of an arc of a circle of radius R carries a uniform charge per unit length A The arc subtends a total angle 20o, symmetric about the x axis, as shown in the figure (Figure 1). Determine the magnitude of the electric field E at the origin 0. Express your answer in terms of the variables A, 0, R, and appropriate constants. Figure Submit Request Answer PartB Determine the direction of the electric field E at the origin O θο O to the left O to the right Submit Request Answer

Answer 1

Given that The charge density of rod is λ The radius of curvature of wireis AR Consi der a small element ds on the rod and is making an angie The charge on the element ds is dq d? at origin The electricfiel d due to the element ds at the origin is dE And de-kda herek-_ 4ΛΕ λ.ds By resloving dE into x,y components and dE, dEsin& Here only the x- components of dE gives net resultant electricfiel d And ally- components of dE produced by the all small elements on rod will cancel with each other By considering only the x- components From (2) and(3) equations and ds_r.d θ Then dE,--cos θ.dθ The total electricfield produced at origin,isE then E- dE 2Z sin uo