Electrostatic potential is computed for a rodlike macromolecule in salt free solution by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). Afterwards, as a verification, our numerical results for a one dimensional PBE, which corresponds to a long macromolecule are compared with the existing analytical formula in salt free solution, and excellent agreement is found. As a macromolecule has a rodlike shape, a much more real case is considered, which leads to a two dimensional PBE. By comparing the solutions of one and two dimensional PBEs, we drew a conclusion that considering one dimensional PBE cannot describe accurately due to the large discrepancy between two aforementioned solutions. Moreover, by considering the number of elements as 24,832 and 76,800, a sufficient accuracy can be obtained for the cases of two and one dimensional solutions, respectively. The results of this work are related to some surfaces such as stiff fragments of DNA or actin filaments.
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