8 a find the electric field along the z axis of a

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8) (a) Find the electric field along the z-axis of a circular loop centered in the xy plane of radius a carrying a uniform line charge λ 0 for y > 0 and – λ 0 for y < 0. (b) Use the results of (a) to find the electric field along the z-axis of a circular disk of radius a carrying a uniform surface charge σ 0 for y > 0 and – σ 0 for y < 0.
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9) (a) Find the electric field along the z-axis due to a square loop with sides of length a centered about the z-axis in the xy plane carrying a uniform line charge λ . What should your result approach for z >> a? (b) Use the results of (a) to find the electric field along the z-axis due to a square of uniform surface charge σ 0 . What should your result approach for z << a? Hint: Let u = z 2 + x 2 4 du u 2 u z 2 = 2 z tan 1 2 u z 2 z 2 10) A circular loop of radius a in the xy plane has a uniform line charge distribution λ 0 for y > 0 and – λ 0 for y < 0. (a) What is the electric field along the z-axis? (b) Use the results of (a) to find the electric field along the z-axis due to a surface charged disk whose density is σ 0 for y > 0 and – σ 0 for y < 0. Hint: r 2 du r 2 + z 2 3 = r r 2 + z 2 + ln r + r 2 + z 2 ( ) (c) Repeat (a) if the line charge has distribution λ = λ 0 sin φ . (d) Repeat (b) if the surface charge has distribution σ = σ 0 sin φ . 11) Find the electric field everywhere for the following planar volume charge distributions: (a) ρ x ( ) = ρ 0 e x / a −∞ ≤ x ≤ ∞ (b) ρ x ( ) = ρ 0 b x ≤ − a ρ 0 a x b # $ % & % (c) ρ x ( ) = ρ 0 x
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  • Summer '13
  • BenjaminYellen
  • Charge, Electric charge, Fundamental physics concepts, charge density

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