Satellites and other spacecraft travelling through the Earth’s radiation belts c

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 mC during one orbit of the Earth.
a) What is the surface charge density on the satellite’s surface?
b) What is the electric field strength just outside the surface of the satellite?
c) What is the electric field strength just inside the surface of the satellite?
d) What is the electric field strength at a distance of 3.0 m from the center of the satellite?
e) What is the electric field strength at the center of the solid metal satellite?

Explanation / Answer

A)surface charge density= charge/surface area

=-3.6 ×10^-3 / (4×3.14×1.6×1.6) = 0.000112 C/m2

b) E = kq/R^2 = 9×10^9×0.0036/(1.6×1.6)

= 1.266 × 10^7 N/C towards center

c)zero because conducting sphere behaves likes shell and Electric field inside spherical shell is zero

d) The distance 3m is greater than radius,

So E = kq/R^2 = 9×10^9×0.0036/(3×3)

=3.6 × 10^6 N/C towards center

e) zero because conducting sphere behaves likes shell and Electric field inside spherical shell is zero

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