For charged wormlike particles immersed in 1:1 electrolyte solution, a theory is based on approximate analytical solution of the linearized Poisson-Boltzmann (PB) equation. Analytical expressions have been obtained for the electrostatic free energy of a bent cylinder and for the electrostatic contribution to its persistence length. Different regimes of deformation of a wormlike particle lead to different expressions for the electrostatic persistence length. For different regimes, the dependence of the electrostatic persistence length on salinity has been established and compared with that from previously known theories. The theory is applied to solutions of polyelectrolyte chains and to solutions of wormlike micelles of ionic surfactants. Apart from systems considered in this work, the simple electrostatics may be useful in many other engineering applications.