Question

Magnetic field is non conservative.Then how can we define potential energy for magnetic field because potential energy associates with conservative field.plz answer in detail​

Answer 1

Answer:

I found the whole debate very interesting. With reference to the comment of Bejo, I would like to submit the following remark: from analytical mechanics (as exposed, e.g., in Goldstein, "Classical Mechanics" and Lanczos, "The Variational Principles of Mechanics") one is led to assume that the Lorentz force on a single charge q(E+v \times B/c) is monogenic, i.e., it is derivable from a velocity-dependent potential U, which is a function of the particle velocity and of both scalar and vector potentials. Then the Lagrangian is L= T-U, while the conserved quantity is not T+U but the Hamiltonian of the system. Accordingly, one might state that the Lorentz force is "conservative" in this more general sense. Though this view is mathematically consistent, the physical nature of velocity-dependent potentials seems elusive.