Midterm TH 2011 - Phys601/F11/Midterm Take-Home Due in...

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Phys601/F11/Midterm Take-Home Due in class 11/21/11 1. Work independently but can consult any text, etc 2. Return only this exam booklet (8 pages), with boxes filled out. All important steps should be clearly shown, succinctly and neatly. If extra space is needed (it should not be), use the back sides. Do not attach other pages unless you absolutely have to. 3. Send email to me for any clarifications/typos. 4. Parts 1, 2, 3, 7 can be done independently. Possibly some others. 5. 10 parts, O(10) points per part.
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Monopole A particle of mass m and charge q moves in the field of a magnetic monopole. This field is given by B = b r /r 3 , where b is a constant. Assume that the mass m never gets to r = 0. Apart from the Lorentz force, there are no other forces on the mass m. For the first 6 parts, do not use the Lagrangian method. Simply use Newton’s Equations in the original form. 1. Prove directly from Newton’s Equations that the kinetic energy, T = (1/2)mv 2 , is a constant of the motion.
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