Final answer:
The electric potential at the origin (x = 0) is 4.5 V.
Explanation:
The electric potential at a point due to a continuous charge distribution is determined by integrating the electric potential formula. For a uniformly charged rod along the x-axis from x = 2.0 m to x = 5.0 m, the integral expression becomes V = k * λ * ∫(dx/x), where k is Coulomb's constant, λ is the charge density, dx is the charge element along the x-axis, and the integration is performed over the specified limits. Solving this integral yields the electric potential function. Integrating from 2.0 m to 5.0 m, we find that the electric potential at any point along the x-axis is the natural logarithm of the ratio of the upper and lower limits.
However, to find the electric potential at the origin (x = 0), we consider the lower limit of integration as x approaches zero. The natural logarithm of 0 is undefined, but the limit of the electric potential as x approaches 0 is finite and equal to 4.5 V.
This result signifies that the electric potential at the origin is solely dependent on the chosen reference point at infinity. The charge distribution along the rod creates an electric potential that, when evaluated at the origin, is 4.5 V.