Consider n point charges located at the vertices of regular n-sided polygons. the radius of the circle that passes through all of these charges is r. each point has charge 4. take the center of the circle to be the origin of your coordinate system, and take the z-axis to be perpendicular to the plane of the polygon. (1.1) write down the equation for the electric field at any point in space. (1.2) write down the equation for the electric field at any point in the plane of the polygon. (1.3) write down the equation for the electric field at any point on the z-axis (1.4) show that the electric field at the center of the circle is zero when n is even (1.5) show that the electric field at the center of the circle is zero when n is odd. for the following, consider the case n=4. (1.6) write down the equation for the electric potential at any point in space. (1.7) write down the equation for the electric potential at any point in the plane of the polygon. (1.8) write down the equation for the electric potential at any point on the z-axis. (1.9) show that the gradient of your equation for the potential is equal to your equation for the electric field. (1.10) use an applet to find the potential and the electric field in the plane of the charges. (1.11) explain why they look the way that they do. what would the rubber sheet or soap bubble look like? (1.12) use falstad's applet to find the electric flux that comes out of regions that include one of the charges two of the charges, three of the charges, and none of the charges. explain your results in terms of maxwell's equations (1.13) use falstad's applet to find the electric circulation around of regions that include one of the charges, two of the charges, three of the charges, and none of the charges. explain your results in terms of maxwell's equations