notes24 2317

notes24 2317 - ECE 2317 Applied Electricity and Magnetism...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 24 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Stored Energy Stored Energy 1 2 Ev V Ud V ρ 1 2 E V UD E d V =⋅ () 0 Φ∞= Note: Please see the text book or supplementary notes for a derivation. 1 2 Es S S charge formula: electric-field formula: (volume charge density) (surface charge density) Example + - ε r h x V 0 A [m 2 ] Method #1 ± ± 0 0 0 2 0 0 1 2 1 2 E V r Er V E d V V Ex h V Dx h V V h εε ⎛⎞ = ⎜⎟ ⎝⎠ = = Find the stored energy Example (cont.) Example (cont.) [] 2 0 0 1 J 2 V UA h h = 2 00 1 2 A UV h = Or, 2 0 1 2 E UC V = Recall that 0 r A C h = Hence
Background image of page 1

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

View Full DocumentRight Arrow Icon
Example (cont.) Example (cont.) Method #2 1 2 1 2 11 22 AB Ev V s S As Bs SS Ud V dS dS dS ρ ρρ ∫∫ (since we have surface charge in this problem) ε r h x A [m 2 ] A B + + + + + + + + + + + + + ------------------ Example (cont.) Example (cont.) () 1 2 E AA BB A B UQ Q QQ Q =Φ +Φ −Φ Φ 0 00 1 2 1 2 E V CV V = = 0 1 2 E V = 2 0 1 2 E UC V = Example Example v 0 [C/m 3 ] 0 a Method #1 : 1 2 E V UD E d V =⋅ Gauss’s Law: r < a 3 0 2 0 4 3 4 v a Er r ρπ πε ⎛⎞ ⎜⎟ = ⎝⎠ ± 3 0 2 0 4 3 4 v r r = ± r > a Find the stored energy Solid sphere of uniform volume charge density Example (cont.) Example (cont.) ( ) ( ) 2 2 2 0 000 0 0 33 0 sin 2 2 44 VV r r a vv E a UE d V E d V r d r dd r d r ra Ur d r r d r rr ππ θθ φ π == = = =+ ∫∫∫ v 0 [C/m 3 ] 0 a
Background image of page 2
Example (cont.) Example (cont.) Result: 2 5 0 0 4 15 v E Ua ρ π ε ⎛⎞ = ⎜⎟ ⎝⎠ Let: 3 0 0 3 4 3 3 4 v v Qa Q a ρπ = = as 0 E U a →∞ [] 2 0 13 J 20 E Q U a επ = Note: KCL Law KCL Law
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 9

notes24 2317 - ECE 2317 Applied Electricity and Magnetism...

This preview shows document pages 1 - 4. Sign up to view the full document.

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