EE325_quiz_5_sol - NAME: _ I EE325-Fall 2009 Quiz 5 ρ cos...

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NAME: _________________ I EE325-Fall 2009 Quiz 5 1) If ρ φ = 0 cos VV d what is the Laplacian 2 V ? (5 points) (Hint: 11 1 , ( ) z z A A AA A zz φ ρφ ρ ρ ρρ φ ρ ρ ρ φ ∂∂ ∇= + + ∇ = + + aa a A i ) ρ ρ ρφρ φ φρ ρφ ρ φφ =+ + =− = i 2 00 1 () ( ) ( ) 1c o s 1 1 ( s i n ) cos cos 0 V dd 2) A circular loop of radius b that carries a direct current I resides on the xy plane and is centered at origin. Find the magnetic field strength at an arbitrary point on the z -axis. (Hint1: Biot-Savart Law: π 3 4 || I d dl r r H rr . Hint 2: The magnetic field on axis will be in the ˆ z a direction because of symmetry.) (5 points) π ρ π ρ ρ π π φ π φ π φ π ×− = = + = + =⇒ = + v 3 2 3 0 2 22 3 / 2 0 2 2 2 2 3/2 0 4| | ˆˆ ˆ (0,0, ) 4 (The integral will be cancelled, leaving only the term) 4( ) ˆ (0,0, ) ) z z z z z I Ibd z b z zb Ibd z b Ib dz dl r r Hr a H a H + 2 2 2 3/2 ˆ (A/m) 2( ) z Ib a
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NAME: _________________ II EE325-Fall 2009 Quiz 5 1) If = / 0 ra VV e
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This note was uploaded on 02/07/2010 for the course EE 325 taught by Professor Brown during the Fall '08 term at University of Texas at Austin.

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EE325_quiz_5_sol - NAME: _ I EE325-Fall 2009 Quiz 5 ρ cos...

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