Answer all parts please

Problem 1 Consider the figure below. An electron is fired on a straight-line path towards a conducting plate. The plate has a surface charge density o and a radius that is much greater than the distance L. When the electron strikes the plate, it is measured that AK. E.= 10 eV, where AK.E.= Tf T, is the difference between the electron's final kinetic energy and initial kinetic energy. The path of the electron makes an angle 8 with the x-axis and the Electric Field makes an angle of with respect to the negative x-axis. The electron moves a total distance, L, before it strikes the plate. a) b) c) d) e) f) Draw a diagram of the configuration including the co-ordinate system you have chosen. Write the integral equation for the work done on the electron when moving from its initial position to an arbitrary final position a distance 'r' from where it began. Write the integral equation for the potential difference of the system for a path that begins at the electron's initial position and ends at an arbitrary position a distance 'r' from where it began. Determine the equation for the potential difference between the initial position of the electron and an arbitrary position a distance 'r' from where it began. Plot the potential difference from part d) as a function of r. If the electron is initially at rest and L = 1cm determine the surface charge density on the plate as a function of the given parameters. (assume the radius of the plate is much greater than L)