9780030839931, Chapter 31, Problem 1P

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Chapter 31, Problem 1P Problem The classical definition of the magnetic moment m of a Particle of charge -e, due to its orbital motion, was given by Ampère as the average over the orbit of e (r (31.74) Show that our definition, m = reduces to this form by showing from (31.15) that m = 2mc e Σ rᵢ H (31.75) and (31.76) Step-by-step solution Step 1 of 1 From equation 31.15, the total kinetic energy operator is given by T = 2m 1 Σ X Here, mass of the particle is momentum of the particle is distance of the particle from the centre of its orbit is r,and magnetic field is This is also equal to the total energy operator E. Thus, = The magnetic moment of the particle is given by = = (2) Σ 2c e X H X e = Σ r, X X 2c m The term 1 e X H is equal to the velocity of the particle. It is given as Substitute m Σ e X for in the equation m = 2c e X m Σ X m = 2c This relation is obtained when magnetic moment and velocity are represented as m And Therefore, the definition of magnetic moment is classically given as m =