Final answer:
The magnetic field at the center of a spinning uniformly charged spherical shell is zero, regardless of the angular velocity, due to symmetry and cancellation of magnetic moments from opposite sides of the shell.
Step-by-step explanation:
To determine the magnetic field at the center of a spinning uniformly charged spherical shell, we can draw analogies to a similar situation with a circular loop of wire or a spinning disk with a uniform surface charge density. However, in the case of a spherical shell, the configuration is three-dimensional and the symmetry suggests that the magnetic moment due to any small charge element is canceled out by a corresponding element on the other side of the shell. Therefore, regardless of the angular velocity ω, the magnetic field B at the center of the spherical shell is zero.
Using the physics of electromagnetic effects, more specifically the Biot-Savart Law, we can understand that a charged loop generates a magnetic field. However, a full shell, which can be thought of as an infinite number of such loops, results in an internal magnetic field that cancels due to symmetry. Since the shell is spherical, each incremental ring's contribution is balanced by another ring across the sphere's diameter. Hence, the resultant field inside a uniformly charged, nonconducting, spinning spherical shell is B = 0.