Lecture 10 Lecture 10 --CapacitanceCapacitanceMainly chapter 30 Mainly chapter 30 --Tuesday February 14thTuesday February 14th•1st period: review of the exam•Capacitors and capacitance•Capacitors in series and parallel•Calculating the capacitance•Energy stored in an electric field•Capacitor with dielectric (if time)Reading: pages 679 thru 690 (chapter 30) in HRKReading: pages 679 thru 690 (chapter 30) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssign: deadline Fri. Feb. 17th at 11:59pmWebAssign: deadline Fri. Feb. 17th at 11:59pmGraded problems (Ch.29) Graded problems (Ch.29) ––P. 6, 10; (Ch.30) P. 6, 10; (Ch.30) ––E. 7, 12, 23, P. 9, 20E. 7, 12, 23, P. 9, 20Practice problems (Ch. 30): Ex. 25, 35, 37, 39; Prob. 13, 23Practice problems (Ch. 30): Ex. 25, 35, 37, 39; Prob. 13, 2320 40 60 80 1000246Q.1 - 7.9Q.2 - 6.7Q.3 - 7.6Q.4 - 4.8Mean = 67.6Median = 68Sigma = 16Number of studentsScore on test (%)Exam 1 StatisticsExam 1 StatisticsCapacitorsCapacitors•Used to store energy in electromagnetic fields [in contrast to batteries (chemical cells) that store chemical energy].•Capacitors can release electromagnetic energy much, much faster than chemical cells. They are thus very useful for applications requiring very rapid responses.+q−q+q−qSpecificationsSpecificationsMax field: 70 teslaMax field: 70 teslaCapacitor drivenCapacitor driven1.5 megajoules at 10 kV(.44 magnum slug ≈1 kJ)Imax= 20 kA63 T, 15mm, 7/35ms50 T, 24mm, 6/30ms 42 T, 24mm, 100/500ms1 pulse/hour to 63 tesla500 - 800 pulses, then...CapacitorsCapacitors•The energy really is stored in the electromagnetic fields. •In fact, these fields possess energy and momentum, so you might think of the capacitor as a fly-wheel, though it is more common to think of capacitors as the electrical analog of springs.CapacitorsCapacitors•The transfer of charge from one terminal of the capacitor to the other creates the electric field.•Where there is a field, there must be a potential gradient, i.e. there has to be a potential difference between the terminals.qCV=Δ•qrepresents the magnitude of the excess charge on either plate. Another way of thinking of it is the charge that was transferred between the plates.SI unit of capacitance: 1 farad (F) = 1 coulomb/volt(after Michael Faraday)•This leads to the definition of capacitance C:Capacitances more often have units of picofarad (pF) and microfarad (μF)Capacitors connected in parallelCapacitors connected in parallelΔV+q2-q2-q1+q1+(q1+q2)-(q1+q2)ΔV11qCV=Δ22qCV=Δ12 eqqqCV+= Δ()12 eqCC VCV+Δ= Δ12eqCCC=+Capacitors connected in seriesCapacitors connected in series12111eqCCC=+11neq nCC=∑In fact:Energy stored in electric fieldsEnergy stored in electric fieldsdqdU = ΔV × dqqdU dqC=()2221201122QqQUdU dq Q CVCCC== =≡××=Δ∫∫212ouEε=Energy densityA dielectric in an electric fieldA dielectric in an electric fieldElectric dipoles in an electric fieldNon-polar atoms in an electric fieldA dielectric in an electric fieldA dielectric in an electric field0'=+EE EGGGE = E0− E' E' opposes E0Linear materials: E' ∝ E, E' = χeE⇒ E0= (1 + χe)Eχeis the electric susceptibility (dimensionless)A dielectric in an electric fieldA dielectric in an electric fieldLinear materials: E' ∝ E, ⇒ E0= (1 + χe)E0011(1)1eeeeEEEκχχκ⇒= = =++χeis the electric susceptibility (dimensionless)κeis the dielectric constant (dimensionless)ε = κeεοis the permittivityA dielectric in an electric fieldA dielectric in an electric fieldLinear materials: E' ∝ E, ⇒ E0= (1 + χe)E001/If , theneeeoEVQAEV dκκκεΔ=Δ==×oeeQAAC'
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