Let's analyse an infinite sheet of charge, with constant surface charge density. (every thing in brackets is a hint. it seems long, but the answer to each question is short, so dont worry and don't spend too long on any part) feel free to ask me questions. a. 1 pt draw the system. use your physical intuition to guess how the electric field looks (assume σ is positive), and draw the field lines b. what are the symmetries of the system (e. g. translations, rotations, flips)? based 2 pt on these symmetries, what coordinate system(s) would be most useful to describe this system? define coordinates on your diagram. (define to be the coordinate that measures distance perpendicular to the sheet, so that z is parallel to the normal vector of the sheet.) c. 2 pt use the symmetries of the system to show that the electric field e must point in d. [1 pt which symmetry (or 8ymnetnes) lead to the conclusion that e(-2) = e. [2 pt what kind of gaussian surface allows us to determine the electric field e, given the z direction, and depend only on z, i. e. e-e(s)2 e(z)? (see your diagram to check if this makes sense.) the information above? draw it on your diagram. when can we determine the electric field e from the electric flux фе? why do we need to do parts b-d of this question before we do this one? f. [2 pt] use gauss's law to show that the electric field is given by e = above the sheet (ie. z > 0) and by e--匈.* below the sheet (i. e. 0) g. [0 pt what is the field infinitely far away from the sheet? (take the limit → too.)