EXAMPLE 6.7.1 Potential of a Uniform Spherical Shell As an example, let us find the potential function for a uniform spherical shell. Solution: By using the same notation as that of Figure 6.2.1, we have Phi =-Gint (dM)/(s)=-Gint (2pi rho R^2sinTheta dTheta )/(s) __ g is the local acceleration of a mass m due to gravity.On the surface of Earth, its value is 9.8m/s^2 and is primarily due to the mass of the Earth. CHAPTER (Gravitation and Central Forces From the relation between s and 0 that we used in Equation 6.2.5, we find that the pre- ceding equation may be simplified to read Phi =-G(2pi rho R^2)/(rR)int _(r-R)^r+Rds=-(GM)/(r) (6.7.13) where M is the mass of the shell . This is the same potential function as that of a single particle of mass M located at O. Hence , the gravitational field outside the shell is the same as if the entire mass were concentrated at the center. It is left as a problem to show that, with an appropriate change of the integral and its limits, the potential inside the shell is constant and hence, that the field there is zero.