ele401week1

# Ele401week1 - z ρ a a a A cos 4 sin 3 2 − = z z 5 45 2<<<<<< z c and S is the surface of a quarter of a sphere defined by θ r a a A

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Tutorial 1 (ELE 401) 1. Determine the gradient of the following fields and compute its value at the specified point. a) ) . , . , . ( z e V y x 4 0 2 0 1 0 , 5 cos ) 3 2 ( = + b) ) , , ( e T z 0 3 / 2 , sin 5 2 π φ ρ = c) ) , , ( r Q 2 / 6 / 1 , sin sin 2 θ = 2. Find the divergence and curl of the following vectors: a) z y x a a a A cos sin 2 xz xy e xy + + = b) z ρ a a B sin os 2 2 z c z + = c) a a a C θ r sin 2 sin 1 os 2 r r c r + = 3. Evaluate and if: A × A × a) z y x a a a A 2 z y 2 2 xz y x + = b) z ρ a a a A 3 2 3 2 z z + + = c) a a A r cos sin 2 2 r r = 4. Let . Evaluate z ρ a a D cos 2 2 2 + = z a) S d S D b) v dv D over the region defined by 2 0 , 1 1 5 0 < < z , . 5. Verify the divergence theorem: = v S dv d A S A for each of the following cases: a) and S is the surface of the cuboid defined by . z y x a a a A z y y 2 3 2 + + = y x 1 0 1 0 1 0 < < < < < < z , y , x b) and S is the surface of the wedge
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Unformatted text preview: . z ρ a a a A cos 4 sin 3 2 − + = z z 5 45 2 < < < < < < z , , c) and S is the surface of a quarter of a sphere defined by θ r a a A cos sin 2 r r + = 2 / 2 / 3 < < < < < < , , r . 6. Find the flux of the curl of field a a a T θ r cos cos sin cos 1 2 + + = r r through the hemisphere 4 ≤ = , z r ....
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## This note was uploaded on 04/17/2008 for the course ELE 401 taught by Professor Forgot during the Spring '08 term at Ryerson.

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