Show that if the potential in the lagrangian contains velocity-dependent terms, the canonical momentum corresponding to a coordinate of rotation θ of the entire system is no longer the mechanical angular momentum lθ but is given by pθ = lθ − i n ? ri 3∇viu, where ∇v is the gradient operator in which the derivatives are with respect to the velocity components and n is a unit vector in the direction of rotation. if the forces are electromagnetic in character, the canonical momentum is therefore pθ = lθ + i n ? ri 3 qi c ai .

Place several e-field sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. which statement is true? 1-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages. 2-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages. 3-at any point, the electric field is parallel to the equipotential line at that point.