Lecture_07_(Chap.17) - Capacitor Two uniformly charged...

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Capacitor Two uniformly charged metal disks of radius R placed very near each other + Q - Q A single metal disk cannot be uniformly charged: charges repel and concentrate at the edges Two disks of opposite charges, s << R : charges distribute uniformly: Almost all the charge is nearly uniformly distributed on the inner f f th di k littl e will calculate oth inside and surfaces of the disks; very little charge on the outer surfaces. s We will calculate E both inside and outside of the disk close to the center 1
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Step 1: Cut Charge Distribution into Pieces We know the field for a single disk There are only 2 “pieces + Q - Q R z A Q E 1 2 / 0 E + s E - E net 2
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Step 2: Contribution of one Piece 0 / 1 ( d i s k ) 2 QA z E R     A z E + E net 2, 0 / 1 2 E R Left: A s z E - Right: 0 / 1 2 E R  // 1 Q Az Q As z s z 2 00 11 22 / E R R s  0 0 2 2 R Origin: left disk, center Location of disks: z=0, z =s / t d d , Distance from piece to 2 z, ( s-z ) 2 0 E   Does not depend on z 3
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Step 3: Add up Contributions E A z Location: 3 (fringe field) E - + E net 3, 0 / 1 2 QA E R     E 3, Q / A 2 0 1 z s R // 1 Q Az Q s s z 0 3 00 11 22 / E R R z z s   0 2 R R s A Q / s A Q / or s<<R: E R E 0 3 2 R E 0 1 2 For s<<R: E 1 =E 3 0 Fringe field is very small compared to the field inside the capacitor. Far from the capacitor (z>>R>>s): E 1 =E 3 ~1/z 3 (like dipole) 4
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Electric Field of a Capacitor 2 / QA E  Inside: E + E net 0 Q / A s ringe: E - E 1 E 3 2 0 R Fringe: s z Step 4: check the results: 0 Units: C N m /(N C m C 2 2 2 ) / 5
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Clicker Question 1 Which arrow best represents the field at the “X”? A) B) C) E=0 D) E) 6
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Question 2 Which one of these statements is false ? A. The electric field of a very long uniformly charged rod has a 1/ r distance dependence. B. The electric field of a capacitor at a location outside the capacitor is very small compared to the field side the capacitor inside the capacitor. C. The fringe field of a capacitor at a location far away from the capacitor looks like an electric field of a point pp charge. D. The electric field of a uniformly charged thin ring at the center of the ring is zero. 7
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Infinitesimals and Integrals in Science Q Charge distribution is not continuous Charge distribution is not exactly uniform Mathematical idealization gy orks well for macroscopic systems Works well for macroscopic systems Atomic force microscope: scans microscopic structure using variations in charge density on surface 8
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Chapter 16 Electric Potential 9
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Electric and Gravitational Potential Energy 2 m q 2 m 2 F 1 4  0 q 1 q 2 r 2 ˆ r 12 2 ˆ mm F Gr r   q 1 m 1 q q 1 m m r U el 2 1 0 4 r G U grav 2 1 10
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This note was uploaded on 04/23/2011 for the course PHYS 272h taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lecture_07_(Chap.17) - Capacitor Two uniformly charged...

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