ps4 (1) - Massachusetts Institute of Technology Biological...

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Massachusetts Institute of Technology Biological Engineering Division Department of Mechanical Engineering Department of Electrical Engineering and Computer Science 20.330J/2.793J/6.023J/ Fields, Forces and Flows in Biological Systems, Spring 2007 Problem Set #4. Issued: March 9 th (Friday) D u e d a t e : M a r c h 1 6 th (Friday) Problem 1: Electromagnetic Wave Starting from the differential form of Maxwell’s equation in free space (no charge and current), show that E G and B G fields in free space satisfy the following wave equation. 2 222 2 2 2 2 2 1 (, , 1 , i i i i E ) ) E ix y o r z xyz v t B B y o r z v t ⎛⎞ ∂∂∂ ++ = = ⎜⎟ ⎝⎠ = = Use the following vector identity. () - A A ∇× ∇× = ∇ ∇⋅ ∇⋅∇ G GG What is the propagation speed v of this “electromagnetic wave”? Calculate the numerical value. Problem 2: FT-ICR MS Fourier Transform Ion-Cyclotron Resonance Mass Spectrometer (FT-ICR-MS) is the current state-of-the-art mass spectrometer for analyzing biomolecules. It has a very high mass resolving power ( Δ M/M~10 -5 ), which is high enough to detect the mass shift by one mass unit (one proton).
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ps4 (1) - Massachusetts Institute of Technology Biological...

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