Test 3-SP07 - Phys 208 Test 3 April 9, 2007 dt (a + t 2 ) =...

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Phys 208 – Test 3 – April 9, 2007 1.(20 pts) Given the integral 2 () dt at a π −∞ = + , determine the integral 23 (4 ) dt t −∞ + . Hint: differentiate a few times with respect to a and then set a = 4. 2. (20 pts) In the integral 1 2 00 x xy I ed yd x x + + ⎡⎤ = ⎢⎥ ⎣⎦ ∫∫ , make the change of variables y u x = and vxy =+ . a) Determine the Jacobian J for the area so that || dxdy J dudv = . b) Determine the new limits and evaluate the integral. 3.(20 pts) The force acting on a particle of charge q and mass m moving in a magnetic field B G with a velocity v G is given by dv Fq vB m dt = G GG G . Assume the magnetic field is in the z - direction and the motion of the particle is in the xy -plane. a) Show that the magnitude of the velocity is a constant.
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This note was uploaded on 01/08/2011 for the course PHYS 208 taught by Professor J.peat during the Spring '10 term at Missouri S&T.

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