Using the Lagrangian formalism here you will derive Lorentz force formula for a particle moving through an electromagnetic field! The Lagrangian for a classical particle in an electromagnetic field is given by C = -mac'+ -my + ,mz" + q(Ax + yAy + ZAz) -qq where A (r, t) = (Ax, Ay, Az) and o = 4 (r, t) are the vector and scalar eletromagnetic potentials. (a) Obtain the equations of motion for x, y, z. They should yield OA mr = -q at + qr x (V X A) - qVd (b) Use both E = Vo B =VXA at to show that the equation obtained in (a) is the Lorentz force