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Lecture_03_2097

Lecture_03_2097 - Physics 0175 Lecture 3 ► Electric...

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Unformatted text preview: Physics 0175 Lecture 3 (June 24, 2009) ► Electric Fields Due to Continuous Distributions of Charges ► Electric Field and Electric Force ► Examples ► Electric Dipole: Torque, Potential Energy ► Electric Field and Electric Force ► Electric Dipole: Torque, Potential Energy ► Flux of an Electric Field ► Gauss’ Law 1 Where to Go for Help 1. Your Recitation Section. 2. Office Hours: Lecturer: Prof. Brian R. D’Urso E-Mail: [email protected] 315 Allen Hall Office Hours: Monday and Wednesday, 3:00 – 4:00 pm TAs: Shonali Dhingra, [email protected] Office Hours: Tuesday and Thursday, 8:30 pm – 9:30 pm and Friday, 2:00 pm – 4:00 pm Naufer Nusran, [email protected] Office Hours: Tuesday and Thursday, 3:00 pm – 5:00 pm Sui Chi Woo, [email protected] Office Hours: Tuesday and Thursday, 1:00 pm – 3:00 pm 3. Appointment with Lecturer or any TA. 2 Homework Assignment #1 Reading: Chapters: 21, 22, 23 Problems: See WileyPLUS Register as soon as possible. First homework due Thursday night! 3 Electric Field Electric Field: Empirical Definition Consider a test charge q . Then: q q lim F E r r → = • Units: N/C • E does not depend on q . • E is present whether or not you look using a test charge. 4 Ring of Charge The axial components add to produce a net electric field. For the small element of charge dQ corresponding to the arc length ds, the axial component of the electric field at P is: Therefore: ( ) 2 / 3 2 2 2 2 z R z dQ z 4 1 cos R z dQ 4 1 dE + = + = ε π θ ε π 2 2 R z z cos : Note + = θ ( ) k E ˆ R z Qz 4 1 2 / 3 2 2 + = ε π r C A dq 5 Uniformly Charged Disk, Point on the Axis of Symmetry Q = total charge R = radius σ = surface charge density 2 R Q π σ = Strategy: Break up the disk into rings, radius r, width dr. For each ring, the contribution to the electric field at point P is given by our result for a uniformly charged ring. Perform superposition of the electric field contributions by integrating over the radius of the rings. ∫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = = R 2 / 3 2 2 z 2 / 3 2 2 2 / 3 2 z 1 z r dr 2r z 4 E 1 z r dr 2r z 4 1 z r dQ 4 1 dE dr r 2 dA dQ ε σ ε σ πε π σ σ k E ˆ R z z 1 2 2...
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Lecture_03_2097 - Physics 0175 Lecture 3 ► Electric...

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