hw308 - Classical Electrodynamics Physics 6561 Homework 3....

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Classical Electrodynamics Physics 6561 Homework 3. Due: In class on Tuesday, 9/23 1. Force of charged particle with constant velocity (5 points) Two equal charges q move with equal velocity ~v . What is the force acting between the two charges? The distance between the two charges is R and the angle between ~v and ~ R is θ . 2. Gauge invariance of interacting Lagrangian (5 points) We have made the gauge invariance one of the basic principles for writing down the Maxwell Lagrangian. Argue, that the interaction described by the usual Lagrangian L int = - 1 c 2 A μ j μ is also gauge invariant. 3 Scalar field theory in 2-D (10 points) Consider a real scalar field φ in 2 dimensions, described by the Lagrangian density L = 1 2 μ φ∂ μ φ - λ ( φ 2 - φ 2 0 ) 2 . (a) Derive the Euler-Lagrange equation of motion for this field, and the symmetric energy- momentum tensor. The energy momentum tensor is defined as T μν = L ∂∂ μ φ ν φ - g μν L . (b) Find an explicit STATIC solution (eg.
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hw308 - Classical Electrodynamics Physics 6561 Homework 3....

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