(Solved): Problem \#3 In the diagram below, a rod of constant linear charge density \( \lambda \) lies on th ...

Problem \#3 In the diagram below, a rod of constant linear charge density \( \lambda \) lies on the \( \mathrm{x} \)-axis between \( x_{1} \) and \( x_{2} \). (a) Write down an expression for the electric field vector at \( (0, y) \) due to the infinitesimal charge lying between \( x \) and \( x+d x \). Your expression should be in terms of \( x, d x, y \), and \( \lambda \). (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 \( x_{1}=-3 d \), and \( x_{2}=d \). Find the angle between the electric field and the \( +x \) direction for the following locations: (i) \( (0, d) \) (ii) \( (0,3 d) \) (iii) \( (0,9 d) \) (d) Comment on the trend you notice for the three different cases you calculated in part (c). Why might you have expected this without doing the calculation?