Current - Electricity and Optics - Lecture Slides, Slides of Electrical Engineering

Download Current - Electricity and Optics - Lecture Slides and more Slides Electrical Engineering in PDF only on Docsity! 1 LECTURE 15 • Force between Current Carrying Wires • Gauss’ Law for Magnetism • Ampere’s Law • Magnetism in Matter Force between Two Parallel Current Carrying Wires *Parallel currents attract *Anti-parallel currents repel F  = I L  × B  Force between Two Parallel Current Carrying Wires 2/27/12 4 13.5 V I1 I2 , depending on switch position A500~II 21 + parallel wires R1 R2 DEMO 2 2/27/12 5 I1 I1 I2 I2 attraction repulsion Collapse or expansion? Force Between two Parallel Current Carrying Wires 2/27/12 6 Gauss’ Law for Magnetism Since all lines of B are closed loops, any B line leaving a closed surface MUST reenter it somewhere. TRUE IN GENERAL, not just for this “dipole” example ΦBnet =  Bid  A = 0∫ 2/27/12 7 Compare Gauss’ Law for Electric Fields ΦEnet =  Eid  A = Qenclosed εo ∫ •  Calculate field at distance r from wire using Ampere's Law: Ampere’s Law  Bid  l = µoIEnclosed∫ B dl = 0 2π r ∫ µoI 2πrB = µoI B = µoI 2πr 5 Magnetization and “Bound Current” 2/27/12 17 Net current inside the material is zero. We are left with a surface current and therefore a magnetic moment Magnetization and “Bound Current” 2/27/12 18 2/27/12 19 Magnetization and Magnetic Susceptibility 2/27/12 20 Magnetic Materials fall into Three Categories Category m Km Paramagnetism *increase in B is small *aligns with Bapp Order of (+10–5), depends on temperature 1 + # Diamagnetism Decrease in B is small aligns opposite Bapp Order of (–10–5) 1 – # Ferromagnetism High degree of alignment even in weak Bapp positive and large ~ m 6 2/27/12 21 Magnetic Susceptibility m ( )mapp 1BB χ+=  Material m Type Bi – 1.66 x 10–5 diamagnetic Ag – 2.6 x 10–5 diamagnetic Al 2.3 x 10–5 paramagnetic Fe (annealed) 5,500 ferromagnetic Permalloy 25,000 ferromagnetic mu-metal 100,000 ferromagnetic superconductor – 1 diamagnetic (perfect) m negative for diamagnetics, small and positive for paramagnetics, large and positive for ferromagnetics. 2/27/12 22 Al sample orients itself as a weak magnet. Bext Diamagnetic Bext µ# Bi (bismuth) sample orients itself  to Bext app 5 B)101(B  −+= ~ slight increase app 5 B)101(B  −−= slight reduction Practical summary S N Paramagnetic 2/27/12 23 Classify Types of Magnetic Materials: DEMO Use a strong electromagnet to produce Bext . Put samples in Bext .