PHY2049: Chapter 3047Energy Stored in Magnetic FieldÎJust like electric fields, magnetic fields store energyÎLet’s see how this works2102202εμ==EBuEBuElectric field energy densityMagnetic field energy density48Energy of an InductorÎ How much energy is stored in an inductor when a current is flowing through it?Î Start with loop ruleÎ Multiply by i to get power equationÎ Let PL= power stored in inductorÎ Identify energy stored in inductorÎ Similar to capacitor: diiR Ldtε=+LLdU diPLidt dt==212LULidiLi==∫2diiiRLidtε=+22CqUC=Power produced = dissipated + storedPHY2049: Chapter 3049Energy in Magnetic Field (2)ÎApply to solenoid (constant B field)ÎUse formula for B field:ÎCalculate energy density:ÎThis is generally true even if B is not constant()22211022LULi nlAiμ==lrN turns0Bniμ=202LBUlAμ=202BBuμ=LBUuVAlV==2102EuEε=B field E fieldPHY2049: Chapter 3050Energy Calculation ExamplesÎCalculate uBfor earth field, B = 5 x 10-5TÎCalculate uBfor neutron star, B = 108TÎCalculate uBfor magnetar, B = 1011T()252337051010 J/m224 10BBuμπ−−−×==××()28221 37010410 J/m224 10BBuμπ−== ×××()211227 37010410 J/m224 10BBuμπ−== ×××10 32410 kg/mBucρ=×Equivalent mass densityFrom E = mc2PHY2049: Chapter 3051Web Sites on Neutron Stars, MagnetarsÎOriginal magnetar discovery http://science.nasa.gov/newhome/headlines/ast20may98_1.htm http://www.firstscience.com/site/articles/solarflares.aspÎMore recent magnetar discovery (Feb. 2005) http://www.physorg.com/news3112.htmlÎOnline articles on magnetars http://solomon.as.utexas.edu/~duncan/magnetar.html http://www.space.com/scienceastronomy/magnetar_formation_050201.html http://apod.gsfc.nasa.gov/apod/ap041126.htmlÎArticles on neutron stars (second one has videos) http://www.astro.umd.edu/~miller/nstar.html http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.htmlPHY2049: Chapter 3052Quiz on EnergyÎEach circuit has identical values of V, R and L. After the switch has been closed for a long time, which circuit has the largest energy stored in the inductor L? (1) 1 only (2) 2 only (3) 3 only (4) 1 & 2 (5) 2 & 3RRLRRRRLLVVVAnswer is modified from what was given in class.Answers 2 and 3 were acceptedPHY2049: Chapter 3053Gigajoule Magnet at CERNÎCMS experiment at CERN p-p collisions at world’s highest energy in 2009 Hope to discover new particles, find the origin of mass and new fundamental forcesCompact Muon SolenoidPHY2049: Chapter 3054HumanPHY2049: Chapter 3055CMS Experiment MagnetÎLarge central solenoid magnet to study particle production B = 4T, R = 3.15 m, L = 12.5 m UB= 2.6 x 109J = 2.6 gigajoules!!http://www.spacedaily.com/news/energy-tech-04b.html()()2227043.15 12.5224 10BBUlAπμπ−== ×××PHY2049: Chapter 3056Articles on CMS and LHCÎLarge Hadron Collider at CERN http://public.web.cern.ch/public/en/LHC/LHC-en.htmlÎHome page and picture of CMS experiment http://cms.cern.ch/ÎWikipedia articles http://en.wikipedia.org/wiki/Compact_Muon_Solenoid
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