Final answer:
The magnitude of the electric field induced in a region with a decreasing magnetic field is calculated using Faraday's Law of Induction. The field's magnitude is given by 0.05 T/s • r and its direction is tangential to the circular path, with the strength of the electric field being zero in regions where the electric potential is constant.
Step-by-step explanation:
The question is asking for the magnitude and direction of the electric field in a region experiencing a changing magnetic field. According to Faraday's Law of Induction, a changing magnetic field within a cylindrical region induces an electric field. To find the electric field (E) as a function of r, the distance from the center, we can use the formula derived from the Maxwell-Faraday equation for a circular path around the center: E = -∇B/∇t • (2πr), where ∇B/∇t is the rate of change of the magnetic field with time. Given that the magnetic field decreases uniformly from 1.0 T to zero over 20 seconds, ∇B/∇t = -1.0 T/20 s = -0.05 T/s. Therefore, the magnitude of the electric field E is 0.05 T/s • r and its direction is tangential to the circular path, clockwise if viewed along the direction of decreasing magnetic field.
Now, considering the strength of the electric field in a region where the electric potential is constant, it is known that the electric potential is uniform throughout such a region, indicating no change in potential with respect to distance. Consequently, the electric field strength, which is the negative gradient of the electric potential, would equal zero since a constant potential has no gradient.