Satellites and other spacecraft travelling through the Earth\'s radiation belts

Question

Satellites and other spacecraft travelling through the Earth's radiation belts can intercept a significant number of electrons, and the resulting charge buildup can damage electronic components and disrupt communications. Suppose a solid spherical metal satellite 1.6 m in diameter accumulates a total charge of -3.6 mu C during one orbit of the Earth. What is the surface charge density on the satellite's surface? What is the electric field strength just outside the surface of the satellite? What is the electric field strength just inside the surface of the satellite? What is the electric field strength at a distance of 3.0 m from the center of the satellite? What is the electric field strength at the center of the solid metal satellite?

Explanation / Answer

A) surface charge density = change/surface area = -3.6×10^-6/{4×3.14×1.6×1.6} = 1.12 × 10^-7 C/ m^2

B)E = kq/r^2 = -3.6×10^-6 × 9×10^9/(1.6×1.6)

= 12656 N/C towards center

C)E=0 because consuctor will be like spherical shell

D)E= -3.6×10^-6 × 9×10^9/(3×3)

= 3600 N/C towards center of conductor

E) E =0 because consuctor will be like spherical shell

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