Mythological thunderbolts

Classical Mechanics Level 3

According to the legend, Zeus, the king of ancient Greek gods, had the power to create thunderbolts in his hands and throw them at his opponents. Suppose Zeus creates the thunderbolts by bringing his palms very close together and parallel to each other and then inducing equal but opposite charge at each of them. What magnitude charge does he have to induce in nC on each palm for this to be possible?

Details and assumptions

  • Zeus' hands are in air, which has approximately the same dielectric permittivity as vacuum.
  • Zeus' palms can be modeled as rectangular, with the sides \(20~\mbox{cm}\) and \(15~\mbox{cm}\).
  • The threshold for air ionization is \(E = 3 \times 10^6~\mbox{V/m}\)

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