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hw13sol - Flores Michael Homework 13 Due 4:00 am Inst Sonia...

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Flores, Michael – Homework 13 – Due: Apr 27 2004, 4:00 am – Inst: Sonia Paban 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before making your selection. The due time is Central time. 001 (part 1 of 2) 10 points To demonstrate the generation of electromag- netic waves due to oscillations of a current sheet in the yz -plane at x = 0, one first con- siders the following situation. One turns on a steady current flow along the negative y -axis at t = 0. p z I x y 0 The point P is along the negative x - direction. Let ~ B and ~ E be the magnetic and electric field established at P soon after the switching on of the current, respectively. The directions of ~ B and ~ E are 1. ~ B is along the negative y -axis, ~ E is along the positive z -axis. 2. ~ B is along the negative z -axis, ~ E is along the positive z -axis. 3. ~ B is along the positive y -axis, ~ E is along the positive z -axis. 4. ~ B is along the positive z -axis, ~ E is along the negative y -axis. 5. ~ B is along the positive y -axis, ~ E is along the negative z -axis. 6. ~ B is along the positive z -axis, ~ E is along the positive y -axis. 7. ~ B is along the negative z -axis, ~ E is along the positive y -axis. correct 8. ~ B is along the negative z -axis, ~ E is along the negative y -axis. 9. ~ B is along the negative y -axis, ~ E is along the positive y -axis. 10. ~ B is along the negative y -axis, ~ E is along the negative z -axis. Explanation: Basic Concepts Electromagnetic waves. Since the current on the sheet is flowing along the negative y -axis, the magnetic field for neg- ative values of x is directed along the negative z -axis. x y O O z P P E E B B B A C D About point P we may construct a rectan- gular window ABCDA in the xy -plane. As the “front” of the B -field sweeps across the window to the left, it causes a counterclock- wise induced emf, which is generated by the induced emf at the right side of the window from D to A . Since the side DA can be placed at any location between O and P , when the B -field reaches P , there is a companion E - field stretched out from D to A . Notice that the electromagnetic wave is traveling along the negative x -axis, so ~ E has to be directed along the positive y -axis (so that ~ E × ~ B is directed along the correct direction).
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Flores, Michael – Homework 13 – Due: Apr 27 2004, 4:00 am – Inst: Sonia Paban 2 002 (part 2 of 2) 10 points Now consider the current sheet which under- goes the sinusoidal oscillations with a definite frequency where the amplitude of the mag- netic field oscillations in the waves is B max . Consider a book of area A located at P paral- lel to the yz plane. Find the radiation force on the book, if it absorbs one third of the light. 1. 1 2 B 2 max A μ 0 2. 4 3 B 2 max A μ 0 3. 1 3 B 2 max A μ 0 4. 1 6 B 2 max A μ 0 5. 2 3 B 2 max A μ 0 6.
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