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UT Arlington PHYS 1444 - Lecture Notes

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PHYS 1444 – Section 003 Lecture #20AnnouncementsSelf InductanceSlide 4So what in the world is the Inductance?InductorExample 30 – 3Energy Stored in a Magnetic FieldSlide 9Stored Energy in terms of BExample 30 – 5LR CircuitsSlide 13Discharge of LR CircuitsLC Circuit and EM OscillationsSlide 16Energies in LC Circuit & EM OscillationLC Circuit BehaviorsExample 30 – 7LC Oscillations w/ Resistance (LRC circuit)Slide 21Slide 22Wednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu1PHYS 1444 – Section 003Lecture #20Wednesday, Nov. 16, 2005Dr. Jaehoon Yu•Self Inductance•Inductor•Energy stored in a magnetic field•LR circuit•LC Circuit and EM Oscillation•LRC circuitWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu2Announcements•Quiz Monday, Nov. 21 early in class–Covers: CH 29-4 to end of CH 30•UTA Tech Fair today till 3pm–Lots of things to learn and lots of goodies•A colloquium at 4pm this Wednesday–Dr. P. Nordlander from Rice University–About nano material and magnetic field they generate–Extra credit opportunityWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu3Self Inductance•The concept of inductance applies to a single isolated coil of N turns. How does this happen?–When a changing current passes through a coil–A changing magnetic flux is produced inside the coil–The changing magnetic flux in turn induces an emf in the same coil–This emf opposes the change in flux. Whose law is this?•Lenz’s law•What would this do?–If the current through the coil is increasing?•The increasing magnetic flux induces an emf that opposes the original current•This tends to impedes its increase, trying to maintain the original current–If the current through the coil is decreasing?•The decreasing flux induces an emf in the same direction as the current•This tends to increase the flux, trying to maintain the original currentWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu4Self Inductance•Since the magnetic flux B passing through N turn coil is proportional to current I in the coil, we define self-inductance, L:– •The induced emf in a coil of self-inductance L is– –What is the unit for self-inductance?•What does magnitude of L depend on?–Geometry and the presence of a ferromagnetic material•Self inductance can be defined for any circuit or part of a circuite =1H =BNLIF=BdNdtF- =dILdt-1V s A� =1 sW�Self InductanceWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu5So what in the world is the Inductance?•It is an impediment onto the electrical current due to the existence of changing flux•So?•In other words, it behaves like a resistance to the varying current, like ac, that causes the constant change of flux•But it also provides means to store energy, just like the capacitanceWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu6Inductor•An electrical circuit always contain some inductance but is normally negligibly small–If a circuit contains a coil of many turns, it could have large inductance•A coil that has significant inductance, L, is called an inductor and is express with the symbol–Precision resisters are normally wire wound•Would have both resistance and inductance•The inductance can be minimized by winding the wire back on itself in opposite direction to cancel magnetic flux•This is called a “non-inductive winding”•If an inductor has negligible resistance, inductance controls a changing current•For an AC current, the greater the inductance the less the ac current–An inductance thus acts something like a resistance to impede the flow of alternating current–The quality of an inductor is indicated by the term reactance or impedanceWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu7Example 30 – 3 Solenoid inductance. (a) Determine a formula for the self inductance L of a tightly wrapped solenoid ( a long coil) containing N turns of wire in its length l and whose cross-sectional area is A. (b) Calculate the value of L if N=100, l=5.0cm, A=0.30cm2 and the solenoid is air filled. (c) calculate L if the solenoid has an iron core with =40000.What is the magnetic field inside a solenoid?(b) Using the formula aboveBF =B =The flux is, therefore,L =Using the formula for self inductance:L =(c) The magnetic field with an iron core solenoid isB =L =0nIm =0NI lmBA =0NIA lmBNIF=20N Alm20N Alm=( ) ( )7 2 4 224 10 100 0.30 107.55.0 10T m m mHmpm- --״�=�NI lm2N Alm=( ) ( )7 2 4 224000 4 10 100 0.30 100.030 305.0 10T m m mH mHmp- --״�= =�Wednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu8Energy Stored in a Magnetic Field•When an inductor of inductance L is carrying current I which is changing at a rate dI/dt, energy is supplied to the inductor at a rate– •What is the work needed to increase the current in an inductor from 0 to I?–The work dW done in a time dt is–Thus the total work needed to bring the current from 0 to I in an inductor isP =dW =W =Ie =dILIdtPdt =LIdIdW =�0ILIdI =�2012IL I� �=� �� �212LIWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu9Energy Stored in a Magnetic Field•The work done to the system is the same as the energy stored in the inductor when it is carrying current I– –This compared to the energy stored in a capacitor, C, when the potential difference across it is V–Just like the energy stored in a capacitor is considered to reside in the electric field between its plates–The energy in an inductor can be considered to be stored in its magnetic field212U LI=U =Energy Stored in a magnetic field inside an inductor212CVWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu10Stored Energy in terms of B•So how is the stored energy written in terms of magnetic field B?–Inductance of an ideal solenoid without a fringe effect–The magnetic field in a solenoid is–Thus the energy stored in an inductor is –Thus the energy density is –This formula is valid to any region of space–If a ferromagnetic material is present, 0 becomes . L =B =U =u =2012BU Alm=2012Bum=20N A lm0NI lm212LI =2012N Alm2012BAlm20BlNm� �=� �� �Volume VWhat is this?UV=UAl=2012BmWhat volume does Al represent?The volume inside a solenoid!!E densityEWednesday, Nov. 16, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu11Example 30 – 5 Energy stored in a coaxial cable. (a) How much energy is being stored per unit


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UT Arlington PHYS 1444 - Lecture Notes

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