6B Ch 22-Gauss Law

An electric charge q is distributed uniformly

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Unformatted text preview: rge Distribution – another use of the Gauss law •  Select a sphere as the Gaussian surface •  For r> a qin Φ E = ∫ E ⋅ dA = ∫ EdA = εo Q Q E= = ke 2 2 4 πεor r Outside the sphere Example 22-4: Solid sphere of charge. An electric charge Q is distributed uniformly throughout a nonconducting sphere of radius r0. Determine the electric field (a) outside the sphere (r > r0) and (b) inside the sphere (r < r0). •  Select a sphere as the Gaussian surface, r<a •  qin < Q •  qin = ρ (4/3πr3) ρ π qin ΦE = ∫ E ⋅ d A = ∫ E dA = εo E= qin 4πεo r 2 = keQ a 3 r Uniform Charge Distribution •  Inside the sphere, E varies linearly with r –  E → 0 as r → 0 •  The field outside the sphere is equivalent to that of a point charge located at the center of the sphere λ. Field Due to a Line of Charge, cont •  The end view of the field: perpendicular to the curved surface •  The field through the ends of the cylinder is 0 since the field is parallel to these surfaces Field Due to a Line of Charge, final •  Use Gauss Law to find the field qin ΦE = ∫ E ⋅ d A = ∫ E dA = εo λ E ( 2π r ) = εo λ λ E= = 2ke 2πεo r r λ is the linear charge density on the line σσ dQ/dA E must be perpendicular to the plane and must have the same magnitude at all points equidistance from the plane Choose a sma...
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This document was uploaded on 02/21/2014 for the course CHEM 110A 110a at UCLA.

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