In electrostatic systems, a potential difference (i. e, a voltage) always corresponds to an electric field. is this also true about circuits? specifically, does the potential difference between the two terminals of the battery correspond to an electric field anywhere? or do circuits allow us to have "voltages without fields? "

Athin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. a) what is the magnitude of the electric field due to the rod at z = 0? n/c (b) what is the magnitude of the electric field due to the rod at z = infinity? n/c (c) in terms of r, at what positive value of z is that magnitude maximum? r (d) if r = 4.00 cm and q = 9.00 µc, what is the maximum magnitude? n/c