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

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ECE 280 Homework 3 1. Calculate the line integral of ˆˆ () A xy x yx 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 22 20 ; 0 x y Γ⇒ + − = . 2. Find the flux of the field 2 ˆ 2 A xyzx y xy xzz =− + G out of the unit cube described by 01 , , . xyz ≤≤ 3. Given ˆ ˆ cos( ) Ar r θφ =+ 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: . Er Vr =−∇ G GG If the potential field in rectangular coordinates is 2 () 4 ( 1 ) 2 x x z 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: Jr Hr =∇× (Ampere’s Law). If the magnetic field intensity in cylindrical coordinates is given by ( ) ( / ) z ρφ = G G G A/m, find a formula for the current density ( ) G G (in units of A/m 2 ). 6. The divergence of the electric flux density gives the charge density in space:
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This note was uploaded on 11/04/2009 for the course ECE 280 taught by Professor Mukkamala/udpa during the Spring '08 term at Michigan State University.

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