A solid, nonconducting sphere of radius R has a positive charge Q distributed uniformly throughout its volume. Since the sphere is nonconducting, the charge does not migrate to its surface. (a) What is the volume charge density throughout the sphere? (b) Construct a spherical Gaussian surface of radius r inside the sphere, where r ≤ R. How much charge is contained inside the Gaussian surface? (c) What is the area of the Gaussian surface of radius r? (d) The electric field points radially outward at all points within the sphere (and outside too, for that matter). What is the strength of the electric field at a distance r from the center, inside the sphere?
A solid, nonconducting sphere of radius R has a positive charge Q distributed uniformly throughout its volume. Since the sphere is nonconducting, the charge does not migrate to its surface. (a) What is the volume charge density throughout the sphere? (b) Construct a spherical Gaussian surface of radius r inside the sphere, where r ≤ R. How much charge is contained inside the Gaussian surface? (c) What is the area of the Gaussian surface of radius r? (d) The electric field points radially outward at all points within the sphere (and outside too, for that matter). What is the strength of the electric field at a distance r from the center, inside the sphere?
(a) Q/πR2 or 3Q/4πR3 or 4Q/3πR2
(b) Qr/R or Qr2/R2 or Qr3/R3
(c) 4πr2 or 4πr2/3 or 4πr3/3
(d) Qr/4πR3E0 or 4πR3QE0/r or Qr2/4πR2E0