Physics 2102 Jonathan Dowling Lecture 23 THU 15 APR 2010 Review Session Midterm 3 EXAM 03 6PM THU 15 APR LOCKETT 6 The exam will cover Ch 28 second half through Ch 32 1 3 displacement current and Maxwell s equations The exam will be based on HW07 HW10 The formula sheet for the exam can be found here http www phys lsu edu classes spring2010 phys2102 formulasheet3 pdf You can see examples of old exam IIIs here http www phys lsu edu classes spring2009 phys2102 Test3 oldtests pdf F iLBsin Bsin B cos B Highest Torque 90 sin 1 Lowest Torque 0 90 sin 0 180 cos 1 0 cos 1 Right Hand Rule Given Current i Find Magnetic Field B Checkpoints Questions Magnetic field Force on each wire due to currents in the other wires Ampere s Law Find Magnitude of B ds Right Hand Rule Given Current i Find Magnetic Field B The current in wires A B D is out of the page current in C is into the page Each wire produces a circular field line going through P and the direction of the magnetic field for each is given by the right hand rule So the circles centers in A B D are counterclockwise the circle centered at C is clockwise When you draw the arrows at the point P the fields from B and C are pointing in the same direction up and left Right Hand Rule Biot Savart Given i Find B A length of wire is formed into a closed circuit with radii a and b as shown in the Figure and carries a current i a What are the magnitude and direction of B at point P B b Find the magnetic dipole moment of the circuit 0 i 4 R B NiA Lenz s Law Induction and Inductance Faraday s law d B E dt or d B C E ds dt Inductance L N I For a solenoid L 0n2Al 0N2A l Inductor EMF EL L di dt RL circuits i t E R 1 e tR L or i t i0e tR L RL Time Constant L R Units s Magnetic energy U Li2 2 Units J Magnetic energy density u B2 2 0 Units J m3 i Changing B Flux Induces EMF Flux Up RL Circuits Flux Down E iup t 1 e tR L R 1 2 U B t Li 2 1 E2 tR L 2 L 2 1 e 2 R E tR L idn t e R 1 2 U B t Li 2 1 E 2 2tR L L 2e 2 R E tR L iup t e L VL Li E tR L e L E tR L iup t e L VL Li E tR L e L RL Circuits E 2 t Checkpoints Questions Magnitude direction of induced current Magnitude direction of magnetic field inducing current Magnitude of induced emf current Given E ds direction of magnetic field Given B dB dt magnitude of electric field Current inducing EL Largest L Current through the battery Time for current to rise 50 of max value Largest current R L or 2R L or R 2L or 2R 2L When the switch is closed the inductor begins to get charged and the current is i E R 1 e tR L When the switch is opened the inductors begins to discharge The current in this case is then i E R e tR L E LC Circuits q t E C cos t i t q t E C sin t i t q t 2E C cos t 1 2 1 2 U B t Li t L E C sin t 2 2 Units L 2E 2C 2 s 2 C V s 2 V C J VL t Li t L 2E C cos t Units L 2E C s 2 s 2 V V LC Circuits q t E C cos t qmax EC q T imax EC i i t q t E C sin t Frequency f 2 Angular Frequency 2 f Period T 1 f 2 Hertz rad s sec IP IS Damped Oscillations in an RCL Circuit If we add a resistor in an RL circuit see figure we must modify the energy equation because now energy is dU being dissipated on the resistor i 2 R dt q 2 Li 2 dU q dq di U UE UB Li i 2 R 2C 2 dt C dt dt dq di d 2 q d 2q dq 1 i 2 L 2 R q 0 This is the same equation as that dt dt dt dt dt C d 2x dx of the damped harmonics oscillator m 2 b kx 0 which has the solution dt dt k b2 cos t The angular frequency x t xm e 2 m 4m For the damped RCL circuit the solution is bt 2 m q t Qe Rt 2 L cos t The angular frequency R2 1 2 LC 4 L 31 6 q t Q Qe q t Qe Rt 2 L cos t Rt 2 L q t Q 1 R2 2 LC 4 L Qe Rt 2 L The equations above describe a harmonic oscillator with an exponentially decaying amplitude Qe Rt 2 L The angular frequency of the damped oscillator 1 R2 1 2 is always smaller than the angular frequency of the LC 4 L LC R2 1 undamped oscillator If the term we can use the approximation 2 4L LC 31 7 r
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