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Unformatted text preview: Lecture 7 Chapter 16. Matter & Electric Fields
*A Spherical Shell of Charge *A Solid Sphere Charged throughout its Volume *Integrating the Spherical Shell Electric Field of a Spherical Shell of Charge ualitative approach Q ntegration I E of a Sphere Outside Direction: Divide into 6 areas: E of a Sphere Outside Magnitude: E6 E5 E1+E4 E2 E3 1 E of a Sphere Inside Magnitude: E of a Sphere Inside
Implications Fill charged sphere with plastic. Note: E is not always 0 inside – other charges in the Universe may make a nonzero electric field inside. E of a Sphere Inside
What is electric field right at the surface? Integrating the Spherical Shell
R RΔ θ Δθ θ Rcosθ Rsinθ d r Surface area of ring: Electric field at the surface is highly variable in magnitude and direction Need to be >1000 atomic diameters away from surface for equations to work!
⎛ 2π R sin θ RΔθ ⎞ ΔQ = Q ⎜ ⎟ ⎝ ⎠ 4π R 2
RΔθ
2π ( R sin θ ) 2 Integration
⎛ 2π R sin θ RΔθ ⎞ ΔQ = Q ⎜ ⎟ ⎝ ⎠ 4π R 2 R RΔ θ Δθ Uniformly Charged Spherical Shell
Electric Field inside and outside a shell of uniform charge distribution θ Rcosθ Rsinθ ΔE = 1 ( ΔQ )d 4πε 0 (d 2 + ( R sin θ )2 )3 / 2
π d r E= 1Q (r − R cosθ ) sin θ dθ 4πε 0 2 ∫ ⎡(r − R cosθ )2 + ( R sin θ )2 ⎤ 3 / 2 0⎣ ⎦
Field inside: Field outside:
2/1/11 Demo: 5A13 No Internal Field
10 A Solid Sphere of Charge
What if charges are distributed throughout an object? Step 1: Cut up the charge into shells For each spherical shell: R rE A Solid Sphere of Charge
Inside a solid sphere of charge: E= 1 ΔQ ˆ r 4πε 0 r 2 R E r 3 Spherically Symmetric Charge Distribution Example Outside Two uniformly charged plastic spherical shells. Find electric field at 3 cm, 7 cm and 10 cm from the center. E Inside R r 2/1/11 13 4 ...
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 Spring '07
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 Charge, Electric Fields, Electric charge, Spherically Symmetric Charge Distribution, spherical shell

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