Gauss practice (easy)

The earth has a net electric charge. The resulting electric field is, on average, 150 V/m 150~\mbox{V/m} and it is directed toward the center of the earth. What is the magnitude of the Earth's net charge in Coulombs ? You may assume that the charge is uniformly distributed over the Earth's surface and that the earth is a perfect sphere.

  • k = 1 4 π ϵ 0 = 9 × 1 0 9 Nm 2 / C 2 k=\frac{1}{4\pi \epsilon_{0}}=9\times 10^{9}~\mbox{Nm}^{2}/\mbox{C}^{2}
  • The radius of the earth is 6370 km 6370~\mbox{km} .


The answer is 676282.

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