Problem 2: Figure 2 shows a thin rod of length L with total charge Q (distributed uniformly along the rod). Find an expression for the electric field E at point P. Give your answer in component form. a) Figure 2 shows a representative infinitesimal element dy along the rod and the field dE created by this element in point P. If the rod is charged uniformly along its length, what is the amount of charge dq contained in the element dy? Use it to compute the magnitude of the electric field dĒ in point P (make sure to express it in terms of x, y, and constant parameters of the system). L ул LC ▸ IV Edy P de FIG. 2: The scheme for Problem 2 b) Find x and y-components of the field dE (dEx and dEy). You can use angle at the intermediate steps, but eventually express everything in terms of x, y, and constant parameters of the system. Note that one of the components must be negative (which one?). c) Integrate the x-component of de over the rod to find the x-component of the total field, Ex = (insert the limits of integration yourself). The integral that you need to use here is ² dt fdEx (a²+1²)3/2 = ²√²+ where t is the variable of integration, and a is a constant. You need to figure out which of the variables in dEx plays the role of the variable of integration, and what plays the role of constant a. d) Integrate the y-component of de over the rod to find the y-component of the total field, Ey = | dEy. Here, you need to use the integral (41) 3/2

Problem 2: Figure 2 shows a thin rod of length L with total charge Q (distributed uniformly along the rod). Find an expression for the electric field E at point P. Give your answer in component form. a) Figure 2 shows a representative infinitesimal element dy along the rod and the field dE created by this element in point P. If the rod is charged uniformly along its length, what is the amount of charge dq contained in the element dy? Use it to compute the magnitude of the electric field dĒ in point P (make sure to express it in terms of x, y, and constant parameters of the system). L ул LC ▸ IV Edy P de FIG. 2: The scheme for Problem 2 b) Find x and y-components of the field dE (dEx and dEy). You can use angle at the intermediate steps, but eventually express everything in terms of x, y, and constant parameters of the system. Note that one of the components must be negative (which one?). c) Integrate the x-component of de over the rod to find the x-component of the total field, Ex = (insert the limits of integration yourself). The integral that you need to use here is ² dt fdEx (a²+1²)3/2 = ²√²+ where t is the variable of integration, and a is a constant. You need to figure out which of the variables in dEx plays the role of the variable of integration, and what plays the role of constant a. d) Integrate the y-component of de over the rod to find the y-component of the total field, Ey = | dEy. Here, you need to use the integral (41) 3/2