Consider a spherical conductor, with a spherical cavitycentered about the center

Question

Consider a spherical conductor, with a spherical cavitycentered about the center. the conductor has an inner raidus of a,and an outer radius of b, as shown in the figures. inside thecavity, a charge q is placed off center. the total net charage onthe conductor is +2q. 1. Use Gauss's law to find the total charge on the innersurface. 2. Find the total charge on the outer surface. 3. Use Gauss's law to find the eletric field outside theconductor. Consider a spherical conductor, with a spherical cavitycentered about the center. the conductor has an inner raidus of a,and an outer radius of b, as shown in the figures. inside thecavity, a charge q is placed off center. the total net charage onthe conductor is +2q. 1. Use Gauss's law to find the total charge on the innersurface. 2. Find the total charge on the outer surface. 3. Use Gauss's law to find the eletric field outside theconductor.

Explanation / Answer

1.According to Gauss law E= integral of E.dA E= (q/o) E integral of dA = E * (4a^2) or E * (4a^2) = (q/o) or q = o* E * (4a^2) 2.the total charge on the outer surface is qin= * (4/3)b^3 = (q/V) V = (4/3)a^3 qin= (q/(4/3)a^3) * (4/3)b^3 or qin= q * (b^3/a^3) -----------(1) 3.eletric field outside the conductor is E = k * (q/r^2) q from equation (1)

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