In the diagram below, a rod of constant linear charge density à lies on the x-axis between x₁ and X2. (a) Write down an expression for the electric field vector at (0,y) due to the infinitesimal charge lying between x and x + dx. Your expression should be in terms of x, dx, y, and 2. (b) Integrate to get the actual electric field vector at (0,y). The result will not be pretty. (c) Assume for this part of the problem that x₁ = -3d, and x2 = d. Find the angle between the electric field and the +x direction for the following locations: (i) (0,d) (ii) (0,3d) (iii) (0,9d)

In the diagram below, a rod of constant linear charge density à lies on the x-axis between x₁ and X2. (a) Write down an expression for the electric field vector at (0,y) due to the infinitesimal charge lying between x and x + dx. Your expression should be in terms of x, dx, y, and 2. (b) Integrate to get the actual electric field vector at (0,y). The result will not be pretty. (c) Assume for this part of the problem that x₁ = -3d, and x2 = d. Find the angle between the electric field and the +x direction for the following locations: (i) (0,d) (ii) (0,3d) (iii) (0,9d)