58-60. Charged Conductor at Equilibrium

# 58-60. Charged Conductor at Equilibrium - magnitude is...

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Charged Conductor at Equilibrium (1) Consider a conductor with excess charge Q in isolation. The mobile charges (electrons) are rearranged spontaneously until we have ~ E 0 = 0 everywhere inside the conductor. If ~ E 0 = 0 inside the conductor, then Gauss’ law implies that there can be no net flux through any Gaussian surface that is inside the conductor. Hence there can be no net charge in any region inside the conductor. Hence all excess charge must be at the surface, where it produces an electric field ~ E 0 ( ~ r ) on the outside only. E = 0 0 Q E 0 (r) tsl58 – p.1/3

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Charged Conductor at Equilibrium (2) Now place a point charge q near the charged conductor. The electric field produced by q causes a further rearrangement of mobile surface charges until we have again ~ E = 0 in the interior. Locally, the electric field ~ E is perpendicular to the surface of the conductor, and its
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Unformatted text preview: magnitude is proportional to the charge per unit area: E = σ/² . + Q E = 0 E(r) q + + + + + + + tsl59 – p.2/3 Charged Conductor at Equilibrium (3) • Consider a conductor with a cavity and excess charge Q . • Gauss’ law implies that there is no net charge on the surface of the cavity. • The external field is ~ E ( ~ r ) . There is no field in the cavity. • Now place a point charge q inside the cavity. • Gauss’ law implies that there is a charge-q on the surface of the cavity. • Charge conservation implies that there is a charge Q + q on the outer surface of the conductor. • The external field changes to ~ E ( ~ r ) . There is a nonzero electric field field inside the cavity. + Q E = 0 E = 0-q Q+q E = 0 q E (r) E(r) tsl60 – p.3/3...
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58-60. Charged Conductor at Equilibrium - magnitude is...

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