Q9: (30 pts) This is a multi-part question. A charge Q is placed on a short rod of length L. A charge q is placed a distance, r away from the rod. We will derive an expression for the Coulomb force on the charge. A) (5 pts) If both Q and q are negative, will q be repelled, or attracted to the rod? B) (7 pts) Draw a diagram of this problem, placing the charge in such a way that the Coulomb force will only be in one dimension. How does this added symmetry reduces the electric field to being in a single direction (i.e., ✰, or ŷ). C) (8 pts) Write the correct integral form of Coulomb's law (E), and the Coulomb force (F) equation necessary to solve this problem. Write out the necessary substitutions for r and dq. Then write out the integral for solving the electric y, not r. field. Make sure r is written in terms of Cartesian coordinates, i.e., x and D) (5 pts) Evaluate the integral with the appropriate limits for the rod. Then substitute this expression into the Coulomb force equation to obtain the final result. E) (5 pts) Consider if the charge Q was a point charge, instead of being distributed on a rod. Describe how two point charges of the same magnitude and separation is different than the interaction between a rod and a point charge. (Hint: you can demonstrate your reasoning by plugging some values into the equation you obtained in part D and comparing it with the Coulomb force for point charges.)

Q9: (30 pts) This is a multi-part question. A charge Q is placed on a short rod of length L. A charge q is placed a distance, r away from the rod. We will derive an expression for the Coulomb force on the charge. A) (5 pts) If both Q and q are negative, will q be repelled, or attracted to the rod? B) (7 pts) Draw a diagram of this problem, placing the charge in such a way that the Coulomb force will only be in one dimension. How does this added symmetry reduces the electric field to being in a single direction (i.e., ✰, or ŷ). C) (8 pts) Write the correct integral form of Coulomb's law (E), and the Coulomb force (F) equation necessary to solve this problem. Write out the necessary substitutions for r and dq. Then write out the integral for solving the electric y, not r. field. Make sure r is written in terms of Cartesian coordinates, i.e., x and D) (5 pts) Evaluate the integral with the appropriate limits for the rod. Then substitute this expression into the Coulomb force equation to obtain the final result. E) (5 pts) Consider if the charge Q was a point charge, instead of being distributed on a rod. Describe how two point charges of the same magnitude and separation is different than the interaction between a rod and a point charge. (Hint: you can demonstrate your reasoning by plugging some values into the equation you obtained in part D and comparing it with the Coulomb force for point charges.)