Electromagnetic Field Emf

1. Conjugate momenta:
The conjugate momenta are given by: 2. Hamiltonian:
The Hamiltonian is the Legendre transform of the Lagrangian: Substituting for and simplifying the expression, we get: which matches option (D).
3. Equations of motion:
The equations of motion follow from the Hamiltonian dynamics. For , we have: which matches option (A). Similarly, for , we get: which matches option (B). For , we get: which matches option (C). Thus, the correct answers are (B), (C), and (D).