Lecture_06

Lecture_06 - A Uniformly Charged Thin Ring Distance...

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Distance dependence: Far from the ring ( z >> R ): Close to the ring ( z << R ): E z = 1 4 !" 0 Qz R 3 E z ~ z R 2 + z 2 ( ) 3/2 ! R 2 ( ) 3/2 = R 3 2 0 4 1 z Q E z = E z ~1/ z 2 A Uniformly Charged Thin Ring E z = 1 4 0 Qz R 2 + z 2 ( ) 3/2
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A Uniformly Charged Disk A = ! R 2 E z = ( Q / A ) 2 0 1 " z R 2 + z 2 ( ) 1/2 # $ % % ' ( ( Close to the disk (0 < z < R) E z ! ( Q / A ) 2 " 0 1 # z R $ % ' ( ) E z = 1 2 0 Q R 2 # $ % ' ( 1 ) z R 2 + z 2 ( ) 1/2 * + , , - . / / Along z axis Approximations: E z ! ( Q / A ) 2 0 If z / R is extremely small Very close to disk (0 < z << R)
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Field Far From the Disk ! E = 1 2 ! 0 ( Q / A ) 1 ! z ( R 2 + z 2 ) 1/2 " # $ % ' z ( R 2 + z 2 ) 1/2 = z z (1 + R 2 z 2 ) 1/2 ! 1 ! 1 2 ( R 2 z 2 )... Exact For z>>R ! E " 1 2 0 ( Q / A ) 1 2 R 2 z 2 = 1 4 "! 0 Q z 2 Point Charge
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Uniformly Charged Disk Edge On
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s << R : charges distribute uniformly: + Q - Q s A single metal disk cannot be uniformly charged: charges repel and concentrate at the edges We will calculate E both inside and outside of the disk close to the center Two uniformly charged metal disks of radius R placed very near each other Almost all the charge is nearly uniformly distributed on the inner surfaces of the disks; very little charge on the outer surfaces. Capacitor
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Lecture_06 - A Uniformly Charged Thin Ring Distance...

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