Download Physics 110B: Homework 10 Problems and Solutions and more Assignments Psychology in PDF only on Docsity! Phys 110B: Problems for HW 10 C. Gwinn March 4, 2009 The final will cover the material covered by this homework set. However, the homework is not to be turned in, and will not be graded. Solutions will appear on eres. 1 HW 10 Problem 1 Consider a power plant, which produces power (or equivalently, energy per unit time) Pgen. This power can be expressed as any emf εgen and current I, so long as εgenI = Pgen. The power is transmitted, via power lines with total resistance Rline, to the city, where it develops power Pload in a load resistor. R line /2 R line /2 R load E a) Show that the minimum power is lost in the power lines for εgen as large as practical. b) For some large (but finite) εgen, and fixed Rline, find the load resistance Rload in the city that will develop maximum power. What is the maximum efficiency of power transmission, in this situation? For fun, try comparing your results with information on power transmission on the web. Hint: see Griffiths 7.5. This is a variation of that problem. 2 HW 10 Problem 4 Two surface currents flow in opposite directions, in planes parallel to the x − y plane. A current +K0ŷ flows at z = +h. A current −Koŷ flows at z = −h. 1 a) Find the magnetic field for this configuration. Give magnitude and direction. Explain your reasoning. K0 K0 z y K0 K0 z x y x View from +y View from +x b) Evaluate the Maxwell stress tensor in the region between the two currents. Find the magnetic force per unit area on the upper current sheet. 3 HW 10 Problem 3 a) Consider a magnetized object of volume V , with uniform magnetization ~M . Far away from this object, the magnetic field is approximately a dipole field. What is the dipole moment for that field, ~m? b) The field outside a uniformly magnetized sphere is purely a dipole field. You can prove this fact using orthogonal functions (you need not do so here). For a sphere of radius a and uniform magnetization vecM , what is the dipole moment? What is the surface current ~K, as a function of co-latitude θ on the sphere? Is there any current density ~J? 4 HW 10 Problem 4 A spherical shell of radius a has total charge +Q and rotates with angular speed Ω about the z-axis. ! Q 2
