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) }]
- 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]