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HW03_FS09 - ECE 280 Homework 3 1 Calculate the line...

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ECE 280 Homework 3 1. Calculate the line integral of ˆ ˆ ( ) ( ) A x y x y x y = + + G over the circular path from the point (x1, y1, z1)=(0, 2, 0) to the point (x2, y2, z2)=(2, 0, 0), defined by 2 2 2 0; 0; 0 x y x y Γ ⇒ + = . 2. Find the flux of the field 2 ˆ ˆ ˆ 2 A xyzx y xy xzz = + G out of the unit cube described by 0 1, 0 1, 0 1. x y z 3. Given ˆ ˆ cos( ) A rr θ φ = + G , evaluate A dS G G i v over a hemisphere of radius 4, 0. z 4. The gradient of the electrostatic potential gives the electric field intensity in space: ( ) ( ). E r V r = −∇ G G G If the potential field in rectangular coordinates is 2 ( ) 4( 1) 2 V r x xz = + G V, find the electric field intensity at the point P(2, -5, 2). 5. The curl of the magnetic field intensity gives the current density in space: ( ) ( ) J r H r = ∇× G G G G (Ampere’s Law). If the magnetic field intensity in cylindrical coordinates is given by ( ) ( / ) H r z ρ φ = G G G A/m, find a formula for the current density ( ) J r
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