PS01-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Problem Set 1 Due: Tuesday, February 11 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 and section 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 One Introduction to Teal, Coulomb’s Law and Electric Fields W01D1 T Feb 4 Faraday’s Law Exploration W01D2 W/R Feb 5 Introduction to Teal, Fields, Coulomb’s Law, Electric Fields, Discrete Charge Distributions W01D3 F Feb 7 PS01: Coulomb’s Law Reading Course Notes: Chapter 1.1-1.7, 2.1-2.7 Week Two: Gauss’s Law Problem Set 1 Due Tuesday Feb 11 at 9 pm W02D1 M/T Feb 10/11 Electric Dipoles and Continuous Charge Distributions Reading Course Notes: Sections 2.9-2.13, 2.14.5-2.14.6 W02D2 W/R Feb 12/13 Gauss’s Law Reading Course Notes: Sections 3.1-3.2, 3.6, 3.7, 3.10 W02D3 F Feb 14 PS02: Gauss’s Law Reading Course Notes: Sections 3.6, 3.7, 3.10PS01-2 Problem 1: Vectors. ONLINE. This problem must be submitted online at https://lms.mitx.mit.edu/. You will be given randomly generated values of the vector components unique to you when you attempt this problem online. Given two vectors A = Axˆi + Ayˆj + Azˆk and B = Bxˆi + Byˆj + Bzˆk, calculate (a) C = 2A +B xC = ; yC = ; zC = (b) D =A − 3B xD = ; yD = ; zD = (c) ⋅A B A ⋅B = (d) E =A ×B xE = ; yE = ; zE = (e) What is the angle θ between A and B? Give your answer in degrees. θ= _____________ degrees (f) Find a unit vector ˆe perpendicular to A and B. xe = ; ye = ; ez= Problem 2: Triangle of Charges. ONLINE. This problem must be submitted online at https://lms.mitx.mit.edu/ . You will be given randomly generated values of the three charges unique to you when you attempt this problem online. Three charges lie on the vertices of an isosceles right triangle, as shown in the sketch. The charge q1 is at the origin of the xy-coordinate system, the charge q2 is at (x, y) = (d,0), and the charge q3 is at (x, y) = (0,d). The point P is located on the hypotenuse of the right triangle at (x, y) = (d / 2,d / 2).PS01-3 (a) What is the electric field E at point P? Give the x and y components of the field. For submitting online, use the values of the three charges provided by the edX engine, d = 10 m and ke= 9 × 109N ⋅ m2/ C2. In your numerical submission, you will find that the x and y components of the electric field at P will always be between −500 V/m and +500 V/m. (b) Below we show grass seeds plots of the electric field configurations for the various charge possibilities. Which of these corresponds to the combination of charges given to you by the edX engine? Note that the order of the images below may be different online as compared to this printable version. (1) (2) (3) (4)PS01-4 Problem 3: Subatomic Forces. WRITTEN. You must hand in a written solution to this problem. You may check your numerical answers online, if you wish, but this is not required. (a) In the domain of elementary particles, a natural unit of mass is the mass of the nucleon, that is, a proton or a neutron, the basic massive building blocks of ordinary matter. Given the nucleon mass as 1.67 × 10−27kg and the gravitational constant G as 11 2 26.67 10 N m kg−−×⋅⋅, compare the gravitational attraction of two protons with their electrostatic repulsion. That is, compute the ratio of their gravitational attraction Fg at a separation r to their electrostatic repulsion Fe at that same distance r. Take 922910 /ek x Nm C=. This shows why we call gravitation a very weak force. Numerical check (optional): if you chose to check your answer online, you will be entering a number with a large negative exponent for your answer. If you are unsure of how to do that, first review the material that explains how to enter answers in the edX platform. You will find that material in the Introduction section in the MITx 8.02r residential course page https://lms.mitx.mit.edu/ . FgFe= _______________ (b) The distance between the protons in the helium nucleus could be at one instant as much as small as 1510 m−. How large is the force of electrostatic repulsion Fe between the two protons at that distance? Even stronger is the nuclear force that acts between any pair of hadrons (including neutrons and protons) when they are that close together. Feat r = 10−15 m= ___________ NPS01-5 Problem 4: Balancing Forces. WRITTEN. You must hand in a written solution to this problem. You may check your answers online either numerically, symbolically, or multiple choice, if you wish, but this is not required. The center of a massless balance beam of length 2l rests on a pivot point, as shown in the figure. There are two massless charges glued to the balance beam, a charge q+ at the center of the beam, and a charge q− at the left end of the beam. A distance h below the balance beam, there is a third charge q+, which is fixed in place. There is a mass of mass m hanging from the balance beam, at a distance x from the center. Gravity acts on this mass m. (a) Find
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