Newton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity." The electric field was defined as E = Fon q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g→ of a point mass? Write your answer using the unit vector r^, but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector r^, and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer.   A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as ρ=ρ0(1−r/2R), where ρ0 is the density at the center. Determine ρ0 in terms of M and R.     Gauss's law for gravity: integral ∮g →⋅ dA =−4πGMin Find an expression for the gravitational field strength inside the planet at distance r < R.

A coaxial cylinder of length L = 5 m consists of two cylindrical shells of radii a = 15 cm and b = 20 cm, respectively (see figure). The charge of the inner cylinder shell is Q = + 17.7 μC while the outer shell charge is Q = -17.7 μC. Find the electric field strength at: rc = 10 cm, rd = 18 cm, and re = 25 cm! Please write your answer neatly and readable as well :)

In the early 1900's Robert Millikan discovered the peculiar property that charge came in little packets, no smaller than e = 1.602 x 10-19 C -- he had measured the charge of the electron. Here's (roughly) how he did it.  He removed an electron from an initially neutral droplet of oil with diameter 0.5 ??μm. In a vacuum, he positioned the droplet between two metallic plates separated by 6 mm and fiddled with the potential (voltage) across the plates until the droplet would hover against the force of gravity. Droplets of this size with +e charge would hover, but only for a particular voltage (otherwise they would sink or rise).  Given the parameters stated here, and the fact that the density of the oil was 831 kg/m3, what was the voltage that made the droplets hover? (give your answer with 0.1 V precision)