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110210_hw4 - a carrying a uniform current of density j...

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February 10, 2011 PHYS 4132 Homework 4 Due date: February 17, 2011 1. A conducting loop of area A and total resistance R is suspended by a torsion spring of constant k in a uniform magnetic field B = B e y . The loop is in the yz plane at equilibrium and can rotate about the z-axis with moment of inertia I . The loop is displaced by a small angle θ from equilibrium and released. Assume the torsion spring is non-conducting and neglect self-inductance of the loop. a. What is the equation of motion for the loop in terms of the given parameters ? b. Sketch the motion and label all relevant time scales for the case when R is large. c. What type of motion does the loop undergo ? 2. Consider a long straight cylindrical wire of electrical conductivity σ and radius
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Unformatted text preview: a carrying a uniform current of density j . Calculate the magnitude and direction of the Poynting vector at the surface of the wire. 3. Consider an infinite parallel-plate capacitor, with the lower plate at z= -d/2 carrying the charge density – σ, and the upper plate at z= +d/2 carrying the charge density +σ. a. Determine all nine elements of the stress tensor, in the region between the plates and show your answer in form of a matrix. b. Using the stress tensor, calculate the force per unit area on the top plate. 4. Using Maxwell’s stress tensor, determine the net force on the upper hemisphere of a uniformly charged solid sphere of radius R and charge Q....
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