An insulator in the shape of a spherical shell is shown in cross-section above.

Question

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 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 C (1 C = 10-6 C). (You may assume that the charge is distributed uniformly throughout the volume of the insulator). What is Ey, the y-component of the electric field at point P which is located at (x,y) = (0, -5 cm) as shown in the diagram?

Explanation / Answer

Net charge enclosed inside the larger sphere is plainly Q (2Q from the outer and inner spheres, plus -Q from the middle sphere). Consider an imaginary sphere, radius r, such that r > R3 + a, enclosing the other 3 spheres; charge enclosed in this sphere is still Q. Accordingly, flux coming out of this imaginary sphere is Q/eo. But, field E being symmetric over this surface, F = ? E • da = E ? da = E A = 4p r² E. Thus, 4p r² E = Q/eo Solving for E, E = Q/(4p r² eo). This expression gives field strength at any distance r, provided that r > R3 + a. Gauss' Law can be used as well to find E in the region of space inside the outer sphere. For instance, at any distance r such that R2 + a

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.