Problem 5 (40 points): Spoiler alert: Using the Lagrangian formalism here you will derive Lorentz force formula for a pa

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Problem 5 40 Points Spoiler Alert Using The Lagrangian Formalism Here You Will Derive Lorentz Force Formula For A Pa 1 (39.79 KiB) Viewed 52 times

Problem 5 (40 points): Spoiler alert: 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 1 1 c=zmi? + 5 mij? +3m2+9 (iA+ j4, + 3A:) – qe where A (r,t) = (Ag, Ay, Ay) and 6 = o(r,t) are the vector and scalar eletromagnetic potentials. (a) Obtain the equations of motion for I, y, z. They should yield (20 points) ӘA mra -9 at +qr x (V x A) – 9V (b) Use both E ӘA at Vo B= V XA to show that the equation obtained in (a) is the Lorentz force! (20 points)