1. The problem statement, all variables and given/known data GRAVITATIONAL POTENTIAL AND FIELD DUE TO A “THIN” ROD A thin rod of length L lies along the +y-axis, with one end at the origin (see diagram). Assume: • The rod has length only- no thickness in other directions. • The density of the rod increases proportionally to the y-coordinate: λ = ky, where k is a known constant and λ is in kg/m • Gravitational potential is zero at infinity: φ (∞) = 0 a) Find the gravitational potential φ ( x) at a point (x,0) by direct integration. b) Find the gravitational field g at a point (x,0) by direct integration. 2. Relevant equations dφ = -(G dm)/r 3. The attempt at a solution Still stuck on part a, so that's really the brunt of my question for now (though assistance with part b is more than welcome!). Using the given density function to solve for dm and substituting √(x^2+y^2) for r, I have an expression for dφ: dφ = -(Gk y dy)/√(x^2+y^2) ...but I have no idea how to manipulate this to get a soluble integral :( I've been messing around with partial derivatives and polar coordinates for hours, but nothing seems to work. PLEASE HELP!