Potential theory is the name given to the broad field of analysis encompassing such topics as harmonic and subharmonic functions,
 the Dirichlet problem, Green's functions, potentials and capacity. We wish to gain a deeper understanding of complex dynamics using 
 the tools and techniques of potential theory, and we will restrict ourselves to the iteration of holomorphic polynomials. We will be 
 able to provide an explicit formula for computing the capacity of a Julia set, which in some sense, gives us a finer measurement of 
 the set. In turn, this provides us with a sharp estimate for the diameter of the Julia set. Further if we pick any point $w$ from the 
 Julia set, then the inverse images $q^{-n}(w)$ span the  whole Julia set. In fact, the point-mass measures with support at the discrete 
 set consisting of the roots of the polynomial $q^n - w$, will eventually converge to the equilibrium measure of the Julia set, in the 
 weak*-sense. This provides us with a very effective insight into the analytic structure of the set. Hausdorff dimension is one of the 
 most effective notions of fractal dimension in use. With the help of potential theory and some ergodic theory, we can show that for a 
 holomorphic family of polynomials varying over a simply connected domain $D$, one can gain control over how the Hausdorff dimensions 
 of the respective Julia sets change with the parameter.