TST1_351_S2005

TST1_351_S2005 - Test 1 Physics 351 March 6 2005 Dr...

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Unformatted text preview: Test 1 Physics 351 March 6, 2005 Dr. Gangopadhyaya: As always, to receive full credit you must show your work in a neat, organized and a legible form. Getting an integral from the calculator will not suffice. Binomial Expansion : For x << 1 , (1 + x ) n = 1 + nx + n ( n- 1) 2! x 2 + n ( n- 1)( n- 2) 3! x 3 + ··· 1. (8) Show that ~ ∇ • ‡ ~ A × ~ B · = ~ B • ‡ ~ ∇ × ~ A ·- ~ A • ‡ ~ ∇ × ~ B · . 2. (5) Evaluate the following integral: Z π 2 π 4 δ sin 2 x- 2 3 ¶ dx 3. (5) Given that ~ r = 0 . 2 ˆ i + 0 . 2 ˆ j + 0 . 2 ˆ k , ~ b = 3 . 2 ˆ i + 4 . ˆ j + 7 . 5 ˆ k and V is a volume of radius 0 . 2 units centered at the origin, evaluate the following integral: Z V ‡ ~ r • ~ b- ~ r • ~ r · δ ˆ ~ r- ~ r 2 ! dτ 4. (a) (5) Determine the curl of the vector field G ( ~ r ) = ˆ e φ r and integrate it over an area of a circle of radius R on the x- y plane....
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This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.

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TST1_351_S2005 - Test 1 Physics 351 March 6 2005 Dr...

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