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Unformatted text preview: Create assignment, 53823, Homework 12, Dec 05 at 2:54 pm 1 This print-out should have 17 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making your selection. The due time is Central time. Electron in a magnetic field 34:01, highSchool, multiple choice, > 1 min, fixed. 001 An electron in a uniform magnetic field B in the z direction describes a cyclotron orbit in the xy plane. A physicist along the y axis at point O is trying to detect electromagnetic radiation from the circulating electron using an electric dipole antenna connected in series to an inductor L , variable capacitor C and light bulb of resistance R . As she reorients the antenna and tunes the capacitor the light bulb suddenly lights up. z B x y e O R L C receiving antenna antenna can be oriented in any direction She then maximizes the bulb’s brightness by orienting the antenna 1. along the ˆ ı direction. correct 2. along the ˆ direction. 3. along the ˆ k direction. 4. at any orientation perpendicular to the ˆ direction. 5. at any orientation perpendicular to the ˆ k direction. Explanation: The antenna works best when it is oriented parallel to the electric field vector, or polariza- tion direction, of the propagating EM wave. The electric field of any EM wave propagat- ing in the +y direction can have only x- and z-components (no y-components). Moreover, since the electron circles in the x-y plane, its centripetal acceleration vector has only x- and y-components (no z-components); thus it can only produce EM radiation polarized in the x- and y-directions. Combining the two sets of requirements, EM radiation produced by the circling electron AND propagating in the +y direction must be polarized along the x-direction 002 She then maximumizes the bulb’s brightness by tuning the capacitor to 1. C = eB R m . 2. C = m 2 e 2 B 2 L . correct 3. C = R 2 m eB L . 4. C = e 2 B 2 L m 2 . 5. must know electron’s velocity. Explanation: The electron’s cyclotron frequency is omega = eB/m. Thus it generates EM radiation at this frequency. The bulb will be brightest when the LRC receiving circuit is resonant with this frequency: i.e. ω = 1 √ ( LC ) Equate the two frequencies and solve for C Hewitt CP9 26 R02 34:01, highSchool, multiple choice, < 1 min, fixed. 003 What does a changing electric field induce? 1. Charges 2. Magnetic field correct 3. Light 4. Electrons Create assignment, 53823, Homework 12, Dec 05 at 2:54 pm 2 5. Nothing Explanation: Since a current of charges produces a mag- netic field, it follows that a changing electric field produces a magnetic field....
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This note was uploaded on 11/28/2010 for the course PHY 56705 taught by Professor Turner during the Spring '10 term at University of Texas at Austin.
- Spring '10