homework_01_three_charges

Three Charges

Three charges are fixed in place as shown. The squares in the grid have sides of length [s = 0.24 m]. The magnitude of [q] is [3.0 \mu C], while the magnitude of [Q] is [4.5 \mu C]. What is the magnitude of the net force on q due to the other two charges?

• [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:
  • [ s = 0.24 m]
  • [ h = \sqrt{ 2s^2}]
  • [ i = +q = 3.0 \mu C]
  • [ j = +Q = 4.5 \mu C]
  • [ k = -Q = -4.5 \mu C]
  • [ \theta = \theta_jh = 45^\circ]
• [ F_{i} = \sqrt{ \left| F_{ji,x} - F_{ki,x} \right|^2 + F_{ji,y}^2} ]
  • [ F_{ji,x} = k \frac{ j i}{ h^2} \cos{ \left( \theta \right) } ]
  • [ F_{ji,y} = k \frac{ j i}{ h^2} \sin{ \left( \theta \right) } ]
  • [ F_{ki,x} = k \frac{ j i}{ h^2} ]
  • [ F_{ki,y} = 0 ]