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The value of \( 1/(4\pi\epsilon_0) \) in SI units is about

  • A.\( 3 \times 10^{8} \)
  • B.\( 9 \times 10^{9} \)
  • C.\( 8.85 \times 10^{-12} \)
  • D.\( 4\pi \times 10^{-7} \)

Answer: B

Correct answer: \( 9 \times 10^{9} \)

With \( \epsilon_0 = 8.85\times10^{-12} \) F/m, \[ \frac{1}{4\pi\epsilon_0} = 8.99\times10^{9} \approx 9\times10^{9}\ \mathrm{N\,m^2\,C^{-2}}. \] The 8.85 offered is the permittivity itself rather than the constant built from it, \( 3\times10^{8} \) is the speed of light, and \( 4\pi\times10^{-7} \) is the permeability of free space.

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