homework_04_spheres

Spheres

An insulator in the shape of a spherical shell is shown in cross-section above. The insulator is defined by an inner radius [a = 4.0 cm] and an outer radius [b = 6.0 cm] and carries a total charge of [Q = + 9.0 \mu C]. (You may assume that the charge is distributed uniformly throughout the volume of the insulator). What is [E_y], the [y]-component of the electric field at point [P] which is located at [(x,y) = (0 m, -5.0 cm)] as shown in the diagram?

• Let
  • [a = 4.0 cm = 0.04 m]
  • [b = 6.0 cm = 0.06 m]
  • [Q = 9.0 \mu C]
  • [(x, y) = (0 m, -5.0 cm) = (0 m, -0.05 m) = ]
• Given
  • For sphical insulators with a point charge [Q] at the center:
    • [E = \frac{ Q}{ 4 \pi \varepsilon_0 r^2}]
  • [V_sphere = \frac{ 4}{ 3} \pi r^3]
• [E_y = \frac{ \frac{ Q}{ 4 \pi \varepsilon_0 r^2}}{ V_{sphere_b} - V_{sphere_a}}]