exam1 - PHY 3323 Exam#1(1 Evaluate the following integrals...

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PHY 3323 September 28, 2009 Exam #1 Thucydides V.99 (1) Evaluate the following integrals: a) R 6 2 dx (3 x 2 - 2 x - 1) δ ( x - 3) (7 points) . b) R 5 0 dx cos( x ) δ ( x - π ) (7 points) . c) R 3 0 dx x 3 δ ( x +1) (7 points) . d) R -∞ dx ln( x +3) δ ( x +2) (7 points) . (2) Compute the line integral of ~v = r cos 2 ( θ ) b r - r cos( θ ) sin( θ ) b θ + 3 r b φ around the 3-step path: a) Along the x axis from the origin to b x (7 points) ; b) Counterclockwise along the unit circle of radius 1 in the xy plane from b x to b y (7 points) ; and c) Along the y axis from b y back to the origin (7 points) . d) Check your answer using Stokes’ theorem (7 points) . (3) Suppose the charge density is given in cylindrical coordinates ( s, φ, z ) as ρ = n ks for 0 s R 0 for R < s . a) What are the dimensions of the constant
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This note was uploaded on 12/15/2011 for the course PHY 3323 taught by Professor Staff during the Spring '08 term at University of Florida.

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