Knowing the root distribution in soil is essential for estimating water uptake by plant roots. It is difficult, however, to characterize and model undisturbed root systems. Root development in a two-dimensional potential field is simulated with the dielectric breakdown model (DBM), which implies a similarity between electric discharge and root distribution. A weighted potential gradient with an exponent η was used to create probability distributions of root growth. Each root was generated step-by-step by selecting random numbers from probability distributions. Simulations were performed for point sources and horizontal line sources. In both cases, as η increased, the root system changed from a cluster and dense type to a slender and sparse type and the fractal dimension decreased. For a point source of water, there was a definite pattern of root development toward the source. It is concluded that the DBM effectively describes root development under various water conditions.