Final answer:
The rod is shaped as a quarter-circle, and when analyzing its electric field, the curvature must be considered in polar or cylindrical coordinates, contrasting with the electric field produced by a straight wire. So option 3 is correct.
Step-by-step explanation:
The rod mentioned in the question is uniformly charged and bent into the shape of a quarter-circular arc. Therefore, the shape of the rod can be described as a quarter-circle.
When considering the electric field around such a charged object, the charge distribution on the rod impacts the symmetry of the electric field it produces. If we model the situation by dividing the bent rod into infinitesimally small arc elements, each can be treated as part of a circle in polar or cylindrical coordinates.
This approach is similar to the strategy employed for analyzing the electric field around a straight, uniformly charged wire but adjusted for the curvature of the rod.
The reference to the difference between the shape of a straight wire and that of a charged circular arc in the question's context implies that we consider the variation in the electric field based on the geometry of the charged object.
A straight wire yields a symmetric radial electric field, while a uniformly charged quarter-circle must be considered in polar or cylindrical coordinates because of the curvature.