ECE 280 Homework 3 1. Calculate the line integral of ˆˆ()Axyx yxy=+ +−Gover the circular path from the point (x1, y1, z1)=(0, 2, 0) to the point (x2, y2, z2)=(2, 0, 0), defined by 2220; 0xyΓ⇒+− =≥≥. 2. Find the flux of the field 2ˆ2Axyzxy xyxzz=−+Gout of the unit cube described by 01,,.xyz≤≤3. Given ˆˆcos( )Arrθφ=+G, evaluate A dS∫GGivover a hemisphere of radius 4,0.z≥4. The gradient of the electrostatic potential gives the electric field intensity in space: .ErVr=−∇GGGIf the potential field in rectangular coordinates is 2() 4( 1) 2xxz−GV, 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: JrHr=∇×(Ampere’s Law). If the magnetic field intensity in cylindrical coordinates is given by ( )( /)zρφ=GGGA/m, find a formula for the current density ( )GG(in units of A/m2). 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.