(a) Verify that the Kuzmin potential\

\\\\Phi _(K)(R,z)=-(GM)/(\\\\sqrt(R^(2)+(a+|z|)^(2)))

\ has

grad^(2)\\\\Phi =0

for

z!=0

, and so represents a surface density distribution

\\\\Sigma (R)

in the plane\

z=0

.\ (b) Use Gauss's law to determine

\\\\Sigma (R)

.\ (c) What is the circular orbit speed for a particle moving in the plane of the disk?

1. (a) Verify that the Kuzmin potential K(R,z)=R2+(a+z)2GM has 2=0 for z=0, and so represents a surface density distribution (R) in the plane z=0. (b) Use Gauss's law to determine (R). (c) What is the circular orbit speed for a particle moving in the plane of the disk