The dynamics of the wrapping of a charged flexible microfiber around an oppositely charged curved particle immersed in a viscous fluid is investigated. We observe that the wrapping behavior varies with the radius and Young's modulus of the fiber, the radius of the particle, and the ionic strength of the surrounding solution. We find that wrapping is primarily a function of the favorable interaction energy due to electrostatics and the unfavorable deformation energy needed to conform the fiber to the curvature of the particle. We perform an energy balance to predict the critical particle radius for wrapping, finding reasonably good agreement with experimental observations. In addition, we use mathematical modeling and observations of the deflected shape of the free end of the fiber during wrapping to extract a measurement of the Young's modulus of the fiber. We evaluate the accuracy and potential limitations of this in situ measurement when compared to independent mechanical tests.