PHY 1120, Take-Home Bonus Problem I Due: By Exam I +5 exam points Instructions: This is a "Take Home" Exam Bonus Problem, and it should be treated as an exam problem. That means do not work with a tutor, other students, or any other human being or computer on this problem other than me. I will let you work with a single partner if you choose, but no one else! You and your partner may turn the problem in together. You may not consult any online resources for this problem other than your textbook and classnotes and me! If I even suspect someone of cheating (and no one tells me), I may cancel the whole bonus opportunity for the class! HONOR PLEDGE (Must be signed for your exam to be graded.) In accordance with the Belmont Honor Code, I have neither given nor received unauthorized aid on this exam, and I have no knowledge of another student giving or receiving unauthorized aid. I understand that the Honor Code requires me to notify the professor if either another student or I have broken this pledge. Signed: Signed: We seem to live in a universe with 3 spatial dimensions (x, y, z) and 1 temporal (time) dimension. But that might not be the case! One explanation for why gravity is such a weak force is that it may be "leaking" out into extra dimensions. For the electromagnetic force, let's explore the effects of extra dimensions on the force law. Let's assume that the constant so does not depend on the spatial dimensions. For this problem, you may use Wikipedia or Mathworld (and no other site) to look up relevant geometry formulas, but do not try to find the answers on the internet or discuss the problem with anyone but the instructor or your partner. Use Gauss's Law to derive an equation for Coulomb's Law (or equivalently, the electric field of a point charge Q at a distance of r from the charge) in a spherically symmetric, 4-dimensional space