Final_Exam_Solutions_Spring2011

# Final_Exam_Solutions_Spring2011 - Final Exam Graduate...

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Final Exam: Graduate Electromagnetics II, 95.658 Spring 2011, UMass Lowell, Dr. Baird Part I: Multiple Choice (45 Points) Circle the one best answer to each question. 1. At very high velocities, what role does a particle's rest mass play in its total energy? (a) its rest mass becomes negligible (b) its total energy is still directly proportional to its rest mass (c) its rest mass becomes zero (d) its rest mass is almost completely converted to radiant energy 2. Consider a perfect electric dipole that oscillates such that it emits electromagnetic radiation. In the radiation zone, what is the polarization of the electromagnetic waves emitted? (a) unpolarized (b) circularly polarized (c) linearly polarized parallel to the dipole vector (d) linearly polarized perpendicular to the dipole vector 3. What is the best statement summarizing the effect on an object's length due to frame motion in Einstein's relativity? (a) Rulers always measure the same no matter how they are moving (b) A moving ruler is shorter in its own frame (c) A moving ruler is seen by the stationary observer to be shorter than at rest (d) A moving ruler is seen by the stationary observer to be longer than at rest 4. In the process of deriving radiation expressions from Maxwell's equations, how do we solve the non- homogenous wave equation? (a) Place the sources inside a grounded spherical shell and apply boundary conditions (b) Assume that far away all sources look spherical and sum over spherical harmonics (c) Laplace transform the non-homogenous wave equation (d) Find and use the time-dependent free-space Green function 5. What is the time averaged value of the energy flux of a traveling sinusoidal electromagnetic wave? (a) One half of its peak intensity (b) One half of its average electric field value (c) One fourth of its average electric field value (d) Its peak intensity squared

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6. The norm of the covariant four-momentum P is equal to what? (a) a complicated function of the traditional velocity u (b) mc (c) vmc (d) always a vector 7. In the long-wavelength limit, how does the power scattered by a small conducting sphere in the forward direction compare to the power scattered in the backward direction?
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