EE101 HW1S

EE101 HW1S - Problem 1. In cylindrical coordinate system:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem 1. In cylindrical coordinate system: ± 2 r v T π φ = K where 2 T ω = So ± vr ωφ = K Then transform it into spherical coordinate: ± sin vR θφ = K Problem 2. In cylindrical coordinate system ± 2 = K by applying the curl in cylindrical coordinate using the formula on page 13 in lecture note => 3 vzr ∇× = K ± Then convert P1, P2, P3 into cylindrical coordinate system => , 1 (0,0,0) P = 2 (0, / 3, / 2) o PR = , 3(3 / 4 ,/ 3 , / 4 ) oo R = in cylindrical coordinate (r, φ , z). Then by noticing that the amplitude of the curl of this vector field is only proportional to r, the rank should be P3>P2=P1 Problem 3. a. at R=R m R S vd s K v o = ll 2 2 00 sin ( sin ) 9 o o R R Rd d ππ R θ θθφ ∫∫ = 2 3 2 sin 9 o R dd = 23 9 o R
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
b. By applying the formula of divergence in spherical coordinate (p.13 lecture note) => 1 sin 3 v θ ∇= K i => 2 2 000 1 sin sin 3 o R V vdv R drd d ππ θθ ∫∫ K i φ = 2 22 00 0 sin o R dR d r d ∫∫ ∫ = 23 9 o R π Observe that the two results are the same, so the divergence theorem is verified.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2008 for the course EE 101 taught by Professor Williams during the Fall '07 term at UCLA.

Page1 / 4

EE101 HW1S - Problem 1. In cylindrical coordinate system:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online