PS01-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Problem Set 3 Due: Tuesday, February 25 at 9 pm. If you are in a M/W/F class for 8.02, you will need to register for the course “8.02r-MW Electricity and Magnetism (Monday and Wednesday)”. If you are in a Tuesday/Thursday/Friday class for 8.02, register for “8.02r-TTh: Electricity and Magnetism (Tuesday and Thursday)”. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/ Hand in the six written problems in this set (problems 3-8) in your section slot in the boxes outside the door of 32-082 or 26-152 depending on which is your classroom. Make sure you clearly write your name, section, and table number on your problem set. Submit the two online problems in this set (problems 1 and 2) online. Text: Dourmashkin, Belcher, and Liao; Introduction to Electricity and Magnetism MIT 8.02 Course Notes Revised. Week Three: Problem Set 2 Due Tuesday Feb 18 at 9 pm Electric Potential W03D1 T Feb 18 Monday Schedule: Faraday Law Exploration W03D2 W/R Feb 19/20 Electric Potential, Discrete and Continuous Charges; Configuration Energy Reading Course Notes: Sections Sections 4.1-4.3 W03D3 F Feb 21 PS03: Electric Potential Reading Course Notes: Sections Sections 4.7-4.10 Week Four: Equipotentials Problem Set3 Due Tuesday Feb 25 at 9 pm and Energy; Exam 1 W04D01 M/T Feb 24/25 Potential and Gauss’s Law; Equipotential Lines and Electric Fields Reading Course Notes: Sections 3.3-3.4, 4.4-4.6, 4.10.5 W04D2 W/R Feb 26/27 Exam 1 Review Exam 1 Thursday Feb 27 7:30 pm –9:30 pm W04D3 F Feb 28 No ClassPS01-2 Problem 1: Electric Potential and Electric Potential Energy: The answers to this problem must be submitted online. (Part a) If you place a negatively charged particle in an electric field, the charge will move 1) from higher to lower electric potential and from lower to higher potential energy. 2) from higher to lower electric potential and from higher to lower potential energy. 3) from lower to higher electric potential and from lower to higher potential energy. 4) from lower to higher electric potential and from higher to lower potential energy. (Part b) Two point-like charged objects with charges +Q and −Q are placed on the bottom corners of a square of side a, as shown in the figure. You move a positively charged object that starts from rest from the upper right corner marked A to the upper left corner marked B, ending at rest. Which of the following statements is true? Explain your reasoning. 1) The work done by the electrostatic force on the positively charged object is positive and the potential energy of the system of three charged objects decreases. 2) The work done by the electrostatic force on the positively charged object is positive and the potential energy of the system of three charged objects increases. 3) The work done by the electrostatic force on the positively charged object is negative and the potential energy of the system of three charged objects decreases. 4) The work done by the electrostatic force on the positively charged object is negative and the potential energy of the system of three charged objects increases.PS01-3 Problem 2: Energy Minimization: Answer to this problem must be submitted online. Consider two metal shells of radius R1 and R2, quite far apart from one another compared with these radii. (Part a) Given a total amount of charge Q, which we have to divide between the shells, how should it be divided to make the electric potential energy stored in the resulting charge distribution as small as possible? Find expressions for the charges Q − q shell 1, and charge q on shell 2. [Hint: the energy stored in an isolated shell of charge Q and radius R is U = keQ2/ 2 R. First calculate the potential energy when charge Q − q is placed on shell 1 and charge q placed on shell 2. Then minimize the energy as a function of q. You may assume that any charge put on these shells distributes itself uniformly.] Enter your answers using R _1 for R1, R _ 2 for R2, and Q. Q − q = q = (Part b) When you have found the optimal distribution of charge, what is the potential difference between the shells? Enter your answers using R _1 for R1, R _ 2 for R2, and Q. ΔV =PS01-4 Problem 3: Electric Shock You must hand in a written solution to this problem. You may check your answers online if you wish, but this is not required. It’s winter at MIT and after scuffing across the carpet in your dorm room you reach for the doorknob with your index finger extended and get a tremendous shock. How many excess electrons were on your finger just before you received the shock and what was the potential difference between you and the doorknob? (HINT: Dry air breaks down at an electric field strength of about 3 × 106 V m-1.) Ne= Note that the tolerance for the numerical check has been set very generously since a large range of answers should be acceptable. Problem 4 Energy Stored in a Uniformly Charged Spherical Shell You must hand in a written solution to this problem. You may check your answers online if you wish, but this is not required. Consider a spherical shell of radius R that has charge Q distributed uniformly on the surface. We want to know the potential energy U of this sphere of charge. You can make use of the fact that outside a spherical distribution of charge, the electric field and electric potential is the same as if all the charge were at the center. You will calculate the stored potential energy by determining the work done in assembling the charge distribution. (Part a) If during this charging process, the shell has charge q, how much work does an external agent do in moving an amount of charge dq from infinity and adding it to the shell? Enter your answer in terms of k, q, dq, and R. dU = (Part b) Determine the potential energy stored in the shell when the charge on the shell is Q. (You will need to set up an calculate a simple integral.) Enter
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