Problem 1. A point charges of 1 nanoC is located at (x = −2.0m, y = 0). A second identical point charge is at (x = +2.0m, y = 0). Find the electric field (both magnitude and direction) at the following points of interest and rank them by magnitude (for example E1 > E2 > E3). P1 (x = 0,y = 0), P2 (x = +1.0m,y = 0), P3 (x = +3.0m,y = 0). Problem 2. A rod of length L lies along the x-axis between x=L and x = 2L. An identical rod lies along the y-axis between y=L and y = 2L. Both rods are charged with a uniform positive linear charge density λ. Find the electric field (direction and magnitude) at the origin. Problem 3. A uniformly charged infinite sheet with a surface charge density +σ lies flat in the x-y plane. Find the electric field (magnitude and direction) at the following points of interest: P1 (x = 0,y = 0, z = +d) and P2 (x = d,y = d, z = −d). What is the potential difference DV between the two points? Problem 4. A point charge Q is located at the origin. The center of a uniformly charged spherical shell of radius R lies on the x-axis at x = 5R. The total charge of the shell is −2Q. Find the electric field E and the electric potential V at the center of the shell.