A charged particle is constrained to move in a plane under the influence of a central forc...

A charged particle is constrained to move in a plane under the influence of a central force potential (nonelectromagnetic) , and a constant magnetic field B perpendicular to the plane, so that

Set up the Hamilton–Jacobi equation for Hamilton’s characteristic function in plane polar coordinates. Separate the equation and reduce it to quadratures. Discuss the motion if the canonical momentum pθ is zero at time t = 0.