Lecture_06

Lecture_06 - A Uniformly Charged Disk A = π R 2 E z = ( Q...

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Unformatted text preview: A Uniformly Charged Disk A = π R 2 E z = ( Q / A ) 2 ε 1 − z R 2 + z 2 ( ) 1/2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ Close to the disk (0 < z << R) E z ≈ ( Q / A ) 2 ε 1 − z R ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ E z = 1 2 ε Q π R 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 − z R 2 + z 2 ( ) 1/2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ Along z axis Approximations: E z ≈ ( Q / A ) 2 ε If z / R is extremely small Very close to disk (0 < z << R) Uniformly Charged Disk Edge On Two disks of opposite charges, 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 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 + Q- Q s We know the field for a single disk There are only 2 “pieces ” ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≈ R z A Q E 1 2 / ε E- E + E net Step 1: Cut Charge Distribution into Pieces Step 2: Contribution of one Piece E ≈ Q / A 2 ε 1 − z R ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (disk) Origin: left disk, center E- E + E net s z Location of disks: z=0, z =s Distance from piece to ⊗ 2 z, ( s-z ) Δ q = Q ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ≈ − R z A Q E 1 2 / , 2 ε Left: Right: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ≈ + R z s A Q E 1 2 / , 2 ε Step 3: Add up Contributions...
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This note was uploaded on 04/02/2008 for the course PHYS 272 taught by Professor K during the Winter '07 term at Purdue.

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Lecture_06 - A Uniformly Charged Disk A = π R 2 E z = ( Q...

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