Review Session : Midterm 3Physics 2102Jonathan DowlingCheckpoints/QuestionsCheckpoints/QuestionsMagnetic field?Force on each wire due tocurrents in the other wires?Magnitude of ∫B·ds?The current in wires A,B,D is out of thepage, current in C is into the page. Each wireproduces a circular field line going throughP, and the direction of the magnetic field foreach is given by the right hand rule. So, thecircles centers in A,B,D arecounterclockwise, the circle centered at C isclockwise. When you draw the arrows at thepoint P, the fields from B and C are pointingin the same direction (up and left).A length of wire is formed into a closed circuit with radii a and b, asshown in the Figure, and carries a current i.(a) What are the magnitude and direction of B at point P?(b) Find the magnetic dipole moment of the circuit.RiB!"µ40=µ=NiAInduction and InductanceInduction and Inductance• Faraday’s law: or• Inductance: L=NΦ/I– For a solenoid: L=µ0n2Al=µ0N2A/l• Inductors: EL=−L di/dt• RL circuits: i(t)=(E/R)(1-e-tR/L) or i(t)=i0e-tR/L• Magnetic energy: U=Li2/2; u=B2/2µ0dtdEMFB!"=dtdsdEBC!"=#$rriCheckpoints/QuestionsCheckpoints/QuestionsMagnitude of induced emf/current?Magnitude/direction of induced current?Magnitude/direction of magnetic field inducing current?Given |∫ E·ds| , direction of magnetic field?Current inducing EL?Current through the battery?Time for current to rise 50% of max value?Given B, dB/dt, magnitude of electric field?Largest current?Largest L?R,L or2R,L orR, 2L or2R,2L?When the switch is closed, theinductor begins to get charged,and the current isi=(E/R)(1−e-tR/L).When the switch is opened, theinductors begins to discharge.The current inthis case is theni= (E/R) e-t2R/LMaxwellMaxwell’’s Equations:s Equations:!=•SqdAE0/"!=•SdAB 0idAEdtddsBSC000µ!µ+•=•""!!•"=•SCdABdtddsEDisplacement currentGauss’namelessAmpere-Maxwell’sFaraday’sCheckpoints/QuestionsCheckpoints/QuestionsGiven A, B at top and bottom, flux through curved sides?Given a uniform E(t) in acircle, magnetic field at theedge?Rank integration paths according to ∫B·ds Discharging capacitor: direction ofdisplacement current, magnetic field?Charging capacitor: Which curve is for the B inthe wire, which for B in the capacitor gap?Map points: a,b,c,d into 1,2,3B= Magnetic field induced by E.Is E increasing or decreasing?A parallel-plate capacitor has square plates 1.0 m on a side as in Fig. 32-35. A current of 3.2 A charges the capacitor, producing a uniformelectric field E between the plates, with E perpendicular to the plates.(a) What is the displacement current through the region between the plates?(b) What is dE/dt in this region?(c) What is the displacement current through the square dashed path between the plates?(d) What is B · ds around this square dashed
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