Supplementary Notes for Supplementary Notes for Physics 2 DiscussionPhysics 2 Discussion

Tomoyuki Nakayama a.k.a TomTomoyuki Nakayama a.k.a Tom

I just started to make the notes so I just started to make the notes so don’t expect too muchdon’t expect too much

Fundamentals of Electric & Magnetic Fundamentals of Electric & Magnetic FieldField

Electric Field is produced by Electric Field is produced by charges.charges.

Electric field due to point Electric field due to point charge q is given by:charge q is given by:

E = (1/4E = (1/4ππεε)(q/r)(q/r22) )

(Coulomb’s law)(Coulomb’s law)

If you can choose a closed If you can choose a closed surface on which E is surface on which E is constant, you can useconstant, you can use

EE┴┴A = QA = Qinin//εε (Gauss’s Law) (Gauss’s Law)

Magnetic Field is Magnetic Field is produced by moving produced by moving charges or currents. charges or currents.

Magnetic field due to a Magnetic field due to a moving charge or current moving charge or current element is given by:element is given by:

B = (B = (μμ/4/4ππ)(qvsin)(qvsinθθ/r/r22) )

= = ((μμ/4/4ππ)(I)(IΔΔLsinLsinθθ/r/r22) )

(Biot-Savart Law)(Biot-Savart Law)

If you can choose a If you can choose a closed loop on which B is closed loop on which B is constant, you can useconstant, you can use

BB║║L = L = μμIIin in (Ampere’s Law)(Ampere’s Law)

Application of Gauss’s Law & Ampere’s Application of Gauss’s Law & Ampere’s LawLaw

Electric field due to a Electric field due to a uniform charge uniform charge distribution along a distribution along a long, straight line.long, straight line.

Magnetic field due to Magnetic field due to a steady current in a a steady current in a long, straight wire. long, straight wire.

RLC Series/Parallel AC CircuitRLC Series/Parallel AC Circuit

RLC in SeriesRLC in SeriesI is common. (So we use I I is common. (So we use I as a reference.)as a reference.)ΔΔV across R is in phase V across R is in phase w/ I & w/ I & ΔΔVVRR = RI = RIΔΔV across L is 90º ahead V across L is 90º ahead of I & of I & ΔΔVVLL = X = XLLI.I.ΔΔV across C is 90º V across C is 90º behind I & behind I & ΔΔVVC = X = XCCI.I.

RLC in ParallelRLC in ParallelΔΔV is common. (So we V is common. (So we use use ΔΔV as a reference.)V as a reference.)I in R is in phase w/ I in R is in phase w/ ΔΔV & V & IIRR = = ΔΔV/R.V/R.I in L is 90º behind I in L is 90º behind ΔΔV & V & IILL = = ΔΔV/XV/XLL..I in C is 90º ahead of I in C is 90º ahead of ΔΔV V & I& ICC = = ΔΔV/XV/XCC..

Impedance &Phase Angle of RLC Impedance &Phase Angle of RLC Series/Parallel AC CircuitsSeries/Parallel AC Circuits

RLC in SeriesRLC in Series

Total voltage drop is Total voltage drop is the vector sum of the the vector sum of the voltages across each voltages across each element.element.

RLC in ParallelRLC in Parallel

Total current is the Total current is the vector sum of the vector sum of the currents in each currents in each element.element.