Concentric spherical shells. Charge of uniform density (40 pC/m^2) is distribute

Question

Concentric spherical shells. Charge of uniform density (40 pC/m^2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m^2. What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces? (A) 0.36pi N/C (B) 0.54pi N/C (C) 1.62pi N/C (D) 1.98pi N/C A sphere inside a spherical shell. A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric conducting spherical shell (inner radius = 3.0 cm, outer radius 1 5.0 cm) which has a total charge of -3.0 pC. What is the magnitude of the electric field 4.0 cm from the center of these conductors?

Explanation / Answer

Sphere surface area = 4r²

Charge on inner sphere .. Qi = 40.0*10^-12C/m² x 4(0.01m)² = 5.03*10^-14 C
NET charge on outer sphere Qo = 60.0*10^-12 x 4(0.03m)² = 6.79*10^-13 C

Using Gauss's law .. with a spherical Gaussian surface at 0.02 m enclosing a net charge +5.03*10^-14 C

Flux .. EA = Q /
E x 4(0.02)² = +5.03*10^-14/8.85*10^-12
E = 1.13 N/C = 0.36*pi N/C (Option A)

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