Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius [a = 2.0 cm], length [L = 10.0 m] and carries a total charge of [Q_{inner} = + 8.0 nC] where [1 nC = 10-9 C]. The outer cylinder has an inner radius [b = 6.0 cm], outer radius [c = 7.0 cm], length [L = 10.0 m] and carries a total charge of [Q_{outer} = - 16.0 nC] . What is [E_x], the [x]-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance [r = 4.0 cm] from the origin and makes an angle of [30.0^\circ] with the [x]-axis?

• Let
  • [a = 2.0 cm = 0.02 m]
    • Inner solid cylinder radius
  • [b = 6.0 cm = 0.06 m]
    • Outer cylinder inner radius
  • [c = 7.0 cm = 0.07 m]
    • Ourter cylinder outer radius
  • [L = 10.0 m]
    • The length of each of the cylindars
  • [Q_{inner} = 8.0 n C]
    • total charge of the inner cylinder
  • [Q_{outer} = -16.0 n C]
    • total charge of teh outer cylinder
  • [r = 4.0 cm = 0.04 m]
    • distance from the origin to the point
• Given
  • [E = \frac{ \lambda}{ 2 \pi \varepsilon_0 r}]
    • Electric Filed, line of charge
• [E_x = \frac{ \frac{ Q_{inner}}{ L}}{ 2 \pi \varepsilon_0 r} = 311.485 \frac{ N}{ C}]