ConstantsK= 8.98e9E0= 8.85e-12Charge (e) = 1.602e-19Coulombs Law (superposition)F= k q1q2 /d2ĒCapacitorsConnected to a battery- V is constantDisconnected – Charge (Q) is constantQcharge = CΔV =Capacitance*ΔVoltage C = E0A /d (vacuum no dielectric)C = kE0A /d (dielectric)V = Q/CPotential (Point Charge)V =kqr Electric Potential EnergyUniform FieldUelec=QΔV Uelec=QEdPoint changeUelec = k q 1q 2rEnergy of a charged capacitorUc = 1/2C(ΔVc)2 = 1/2Q2/CElectric Potential (Volts J/C)ΔV=Ed and ΔV=ΔU/qE = kq/r2Current ( I = amps = Coulmbs/s)I = ΔQ/ΔtimeOhms LawV = IRR = ϸL/AWire at new Temperatureϸ = ϸ0 [1+ (α(T-T0)]R = R0 [1+ (α(T-T0)]α = temperature coefficientBatteriesΔVbattery =ƐCurrent Densityj = I/A = nvdePower in CircutsP = I ΔVbatteryPower in resistors (dissipated)Pr = W/Δtime = QΔVr/Δtime Pr=IΔVrP= I2RP =ΔV2/RResistorsSERIES - Req = R1 + R2..etcPARA– Req =(1/R1 + 1/R2…)-1 Capacitors SERIES Ceq =(1/C1+ 1/C2)-1 PARALELL Ceq = C1+C2 RC CircuitTime constant = RCC= Farads, is same as V drawn from battI = ΔQ/ΔtimeMagnetic Fieldμ0 = 1.257E-6 m/ASingle Current LoopB = μ0I/ 2R (R= loop radius)Number of loopsB = μ0NI/2RStraight WireB= μ0I/ 2π rSolenoidB = μ0IN/ L (N= # of turns)Lorentz ForceF=qvBForce Paralell Wiresμ0LI1I2 / 2πdForce on a wireFwire =ILBFwire = qvBsinαPath of a Charge in Field r =mv/qBTorque on current loop τ = (IA)BsinθMotional EMFƐ = vlBInduced CurrentI = Ɛ/R I = vlB/RMagnetic Fluxɸ = AB cosθƐ =Δ ɸ /Δ tƐ =N(Δ ɸ /Δ t) (turns)Greatest at θ=0 degreesMaxwells EquationsE = Q/4π Ɛ0 r2Electromagnetic WavesC= 3E8 m/s (speed of light)ƒ = c/ λTransformersV2 rms = (N2/N1) V1 rmsI2 rms =(N1 / N2 )I1 rmsPwire = (Irms)2RStep up transformer raises voltage but lowers current, step down is oppositeAC Resistor CircutsvR = VR cos 2πƒtiR = IR cos 2πƒtSmall “v”and “i”are instantaneous valuesAnd “V” and “I” are Peak fixed valuesP = IV = I2RPR = ½ I2R R (avg pwr loss with peak IR)Irms = IR / sqrt(2)Vrms = VR / sqrt(2)PR = (IR/ sqrt(2))2 RPR =Irms2 RPR = Irms VrmsvR = iR REMF of AC Voltage Source RADIANSƐ = Ɛ0 cos (2π t / T)Ɛ = Ɛ0 cos (2π f t)Peak Current AC with CIC = (2 π f C) VCEnergy Stored in FieldsCapacitorUC = ½ C (ΔVC)2InductorUL = ½ LI2Induced EMF from inductorvL = L (ΔiL / Δt)Ɛ = Ɛ0 cos (2 π ft)IL = VL / XLVL = 2 π fL ( IL)Single Component ACResistorIR = VR / R (I and E in phase)CapacitorIC = VC /XC ( I leads E)XC = ( 1/ 2π f C)InductorIL = VL / XL (I lags E)XL = 2 π fLRL CircuitTime Constantτ = L/ Ri = I0 (1-e-Rt/L )vL = Ɛe –Rt/L)I0 = Ɛ /RInductor voltage is battery voltage at t=0Instantaneously when turned onInductor voltage is 0 at t= infinityLC circuitf = 1/2π sqrt( 1/LC)Irms = ΔVrms / ZIpeak = Irms* sqrt(2)Vpeak L = 2π f L IPeakVPeak C = 1/2 π f C IPeakDriven RLC circuit Imax = Ɛ0 / Rƒ0 = 1/(2π) sqrt( 1/LC)Resonance (XC = XL)Impedance ZZ= sqrt( R2 + (XL – XC)2 )Imax = Ɛ0 / sqrt( R2 + (XL – XC)2 )Electrical DangerI = ΔV / RtotalC = speed of light = 3E8 m/sN = index of refractionAir – 1Glass – 1.5V = c/nRefractionN1 sin (θ) = N2 sin (θ)Total Internal ReflectionΘc = sin-1 (n2/n1)(n2 ˃ n1) –light comes from n2Thin LensesConverging lens – Focus light on pointAfter lensDiverging lens – Bends light outward,Focal point is before lensThins Lens Equation1/S + 1/S’ = 1/ ƒRadius of curvature = 2/r = 1/fS = Object DistanceS’ = Image Distanceƒ = focal lengthMagnificationVirtual image is NEGATIVEM = h’/ h… = -S’/ SH= Object heightH’ = Image HeightRefractive Power(Diopters)P = 1/ ƒ P = 1/S + 1/S’Magnifying LensLargest θ without magnifying lens =Hobject / nearpoint (25cm if not given)Largest θ with magnifying lens =Hobject / ƒM = θ / θ0 …. = near point (25cm) / ƒθ0 = angle without lensθ = angle with lensMicroscopeM = Mobjective * MeyepieceM = -L/ ƒobj * nearpoint (25cm) / ƒeyepiece“minus sign indicates inverted image”TelescopeM = Mobjective * MeyepieceM = θe / θ0…… = - ƒ0 / ƒeƒ = c / λPolarizationItransmitted = ½ IunpolarizedItransmitted = Iincident cos2 (θ)Distance from central Maximum(DOUBLE SLIT INTERFERENCE)Constructive interferenceD sin(θ) = m λSMA = θ = m λ / dD= split separationDestructive InterferenceD sin(θ) = ( m + ½) λYm = L tan (θ)Θ = y/L… = m λ L / dYm = m λ L / d – Bright FringesL= distance from screenD = split separationM = order (1,2,3…)Ym = (m + ½ ) λ L / d – Dark FringesDiffraction Gratings (NO SMA)D sin (θm) = m λ.λ material = λ vaccum / n.λfilm = λ / nfilmVlight = λmaterial * ƒmaterial ….= c/nThin Film Interference2t = m λ / nConstructive – 0 or 2 Phase changesDestructive – 1 phase change2t = (m + ½) λ / nConstructive – 1 phase changeDestructive – 0 or 2Single Slit Diffraction1st Destructive (dark fringe)(a/2) sin(θ) = (λ / 2)Sin (θ) = (λ / a)A = slit widthWidth of central maxW = 2 λ L / aAngle of FringesΘp =P λ / aP = order of dark fringePosition of Dark Fringe Yp = P λL/aDark fringe interferenceA sin(θ) = p λCircular Aperture DiffractionW = 2 y1… = 2L tan(θ)…= 2.44 λ L /