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PC4274A: Mathematical Methods in Physics III Assignment, NUS, Singapore: The Lagrangian for a particle with charge q and mass m in an electromagnetic field described
University National University of Singapore (NUS)
Subject PC4274A: Mathematical Methods in Physics III Assignment
Posted on: 18th Apr 2024

PC4274A: Mathematical Methods in Physics III Assignment, NUS, Singapore: The Lagrangian for a particle with charge q and mass m in an electromagnetic field described

4. [30 pts]
(a) The Lagrangian for a particle with charge q and mass m in an electromagnetic field described by electric scalar potential φ(r(t), t) and magnetic vector potential A(r(t), t) is
 PC4274A: Mathematical Methods in Physics III Assignment
Obtain the equation of motion of the charged particle from Hamilton’s principle.

 PC4274A: Mathematical Methods in Physics III Assignment

(b) The Lagrangian density of an electromagnetic field with a charge density ρ(r, t) and current density J(r, t) is given by

The Lagrangian of an electromagnetic field is given by a volume integral of the Lagrangian density:

 PC4274A: Mathematical Methods in Physics III Assignment
Show that Hamilton’s principle leads to two of Maxwell’s equations.

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