q02c - KurtRudolph/phys212 GitHub Wiki

q02c

  • [F_{ij} = \kappa \frac{ q_i q_j}{ r^2} \hat r]
    • [ \kappa = \frac{ 1}{ 4 \pi \epsilon_0} = 8.99 \times 10^9 \frac{ Nm^2}{ C^2} ]
    • [ \mu = 10^{-6}]
  • Let:
    • [ d ] be the horizontal distance the two [ Q] charges
    • [ h ] be the vertical distance from charge [ q] and the mid point hoizantal plain between the two [Q ] charges.
    • Charge [ q] have mass [ m]
  • Then
    • [ r = \sqrt{ d^2 + h^2 }]
    • [ \theta = \arctan{ \left( \frac{ h}{ d} \right) }]

(a)

  • Let
    • [ F_g = 9.8 m/s^2 ]
  • [ F_g m = 2 \left( \kappa \frac{ q Q}{ r^2} \sin{ (\theta)} \right) ]
    • solve for [ q]
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