The Lagrangian of a particle of charge q moving with velocity v in a region of space with a scalar potential o and a vector potential A is L = mv² – qó(r, t) + qv · A (r, t) . Show that the Lagrange's equations coincide with components of the Coulomb- Lorentz force that is applied to the charged particle, namely mř = qE + qv x B. It is useful to remember that Lagrange equations are d dL :0. qa € {r, y, z}. %3D dt Ôġ,

The Lagrangian of a particle of charge q moving with velocity v in a region of space with a scalar potential o and a vector potential A is L = mv² – qó(r, t) + qv · A (r, t) . Show that the Lagrange's equations coincide with components of the Coulomb- Lorentz force that is applied to the charged particle, namely mř = qE + qv x B. It is useful to remember that Lagrange equations are d dL :0. qa € {r, y, z}. %3D dt Ôġ,