Write the Euler-Lagrange equations for this system

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Reference no: EM131668675

Question - A particle of mass in and charge q moves in the field of a vector potential A(r, t) = -(E₀ct + B₀z)y^{^}. (Note that we are using the cgs Gaussian units of your text book.) Here E₀ denotes a constant electric field amplitude and B₀ denotes a constant magnetic field amplitude. The initial particle position is r(0) = 0 and the initial particle velocity is r^·(0) = 0.

(a) Determine the Lagrangian L(x, y, z, x^·, y^·, z^·, t) which describes the particle's motion.

(b) Write the Euler-Lagrange equations for this system.

(d) Determine the Hamiltonian H (x, y, z, p_x, p_y, p_z, t) for this system.

(e) Convince yourself that the canonical equations of motion are consistent with results of the Lagrangian analysis. (It is not necessary to repeat your solution.)

Reference no: EM131668675

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