Test2-FS01

# Test2-FS01 - Phys 208 Theoretical Physics Test 2 1(25 pts a...

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Phys 208 – Theoretical Physics – Test 2 (October 22, 2001) 1.(25 pts) a) Suppose you want to transform from Cartesian ( x, y ) to Polar coordinates ( r, θ ). Determine the Jacobian for the area; namely J so that . dxdy J drd = θ b) Express the following integral in polar coordinates ( r θ , θ ) and so evaluate it. I e dxdy xy y = −− 22 2 0 1 0 1 2.(25 pts) Given that , determine the integral . dx yx y 0 2 + = π dx () 3 0 + 3.(25 pts) The force acting on a moving particle in a magnetic field is given by r B , where m is the mass of the particle, q is the electric r r r r Fm dv dt qv B == × charge, and is the velocity. Assume the magnetic field is in the z -direction, r v i.e., , and that the motion is in the ( x, y ) plane. r BB z = \$ a) Show that the velocity is perpendicular to the force and it has a constant magnitude. b) Show that the magnitude of the force is also 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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Test2-FS01 - Phys 208 Theoretical Physics Test 2 1(25 pts a...

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