7e Applied EM by Ulaby and Ravaioli 4. ELECTROSTATICS, Part 2 7e Applied EM by Ulaby and Ravaioli
Electrostatics 2 4. 7 Dielectrics (유전체) 4 Electrostatics 2 4.7 Dielectrics (유전체) 4.8 Boundary conditions (경계조건) 4.9 Capacitance (정전용량) 4.10 Electrostatic energy (정전기장 에너지) 4.11 Image method (영상법)
4.7 Dielectric Materials (유전체)
4.7.1 Polarization (분극) P = electric flux density induced by E ε = ε0εr : permittivity (유전율) ε0 = 8.854·10-12 F/m (진공의 유전율) εr : relative permittivity (비유전율) = dielectric constant (유전상수)
Electric or Dielectric Breakdown (절연파괴) Dielectric Strength (유전강도, 절연내력, 절연강도) Insulation, Electrical insulation (전기절연) 절연강도: 공기 = 30 kV/cm, 팔리스타이린 = 2 MV/cm
Discharge and Arc
Dielectric Breakdown Curve
Dielectric Breakdown Terminology Paschen's law: breakdown voltage vs gas pressure Avalanche breakdown Townsend avalanche Static spark gap Discharge: Dark discharge: no light Glow discharge: a plasma formed by the current through a low-pressure gas Arc discharge: a lightning volt, a single or localized set of discharges Corona discharge: distributed arc discharge Partial discharge: localized discharge in an insulation system Ionization energy: 1-3 eV
4.8 Boundary Conditions (경계조건) - 전기장의 경계조건: 매질 경계면에서 전기장의 접선성분과 법선성분이 만족해야 할 조건 - 접선성분: 폐경로를 따라서 전기장 적분 → 전위차 0 - 법선송분: 폐곡면에서 전속밀도 적분 → 가우스법칙 적용
Summary of Boundary Conditions Remember E = 0 in a good conductor
Field Lines at Conductor Boundary At conductor boundary, E field direction is always perpendicular to conductor surface
4.9 Capacitance (정전용량)
Capacitance For any two-conductor configuration: For any resistor:
아래 구조의 저항으로부터 커패시턴스를 구하라.
Fringing field (누설장) and fringing capacitance (누설 커패시턴스)
커패시터의 직렬/병렬 연결시 합성 정전용량
병렬로 중첩된 콘덴서 콘덴서의 직병렬연결에 의한 정전용량의 계산은, 병렬, 직렬연결 저항계산법과 동일하다.
Application of Gauss’s law gives: Q is total charge on inside of outer cylinder, and –Q is on outside surface of inner cylinder
구형축전기의 정전용량 - 단일 구의 정전용량:
직렬로 적층된 구형 커패시터: 음극면은 무한구면
Tech Brief 8: Supercapacitors For a traditional parallel-plate capacitor, what is the maximum attainable energy density? Mica has one of the highest dielectric strengths ~2 x 10**8 V/m. If we select a voltage rating of 1 V and a breakdown voltage of 2 V (50% safety), this will require that d be no smaller than 10 nm. For mica, = 60 and = 3 x 10**3 kg/m3 . Hence: W = 90 J/kg = 2.5 x10**‒2 Wh/kg. By comparison, a lithium-ion battery has W = 1.5 x 10**2 Wh/kg, almost 4 orders of magnitude greater Energy density is given by: = permittivity of insulation material V = applied voltage = density of insulation material d = separation between plates
A supercapacitor is a “hybrid” battery/capacitor
Users of Supercapacitors
Energy Comparison
4.10 Electrostatic Potential Energy (전기장 에너지)
전하를 이동시키는데 소요된 에너지 전하를 이동시키는데 소요된 에너지
정전기장의 에너지 + 두 식을 합한다. 여기서 V1 = V1,2 + V1,3 + ··· + V1,N
정전기장의 에너지
커패시터에 저장된 에너지 Energy stored in a capacitor
전계강도를 이용한 정전기장 에너지 계산
전기장에 저장된 에너지
Electrostatic potential energy density (Joules/volume) Total electrostatic energy stored in a volume
유전체 손실 1) 커패시터를 이용한 유도
2) 전기장 전력밀도를 이용한 유도
4.11 Image Method Image method simplifies calculation for E and V due to charges near conducting planes. For each charge Q, add an image charge –Q Remove conducting plane Calculate field due to all charges
Image Method Applied to Capacitance Calculation
Image Method: Two-cylinder problem
Image method: two-sphere problem, one sphere grounded 1. First charge: at the center of the left sphere Left sphere: equipotential 2. Second charge: inside the right sphere Let V at the right sphere be zero. 3. Do 2 for the left sphere. Repeat the above.
Image method: two-sphere problem, two spheres floated
Tech Brief 9: Capacitive Sensors
Wheatstone Bridge Formula
Humidity Sensor (습도센서) 습도(수분, 물)에 따른 커패시턴스 변화 측정
Pressure Sensor (압력센서) 압력에 따라 커패시터 극판간격 변화에 따른 커패시턴스 측정
Planar capacitors (평판커패시터) 터치(물체접촉) 센서: 물체유무에 따른 커패시턴스 변화측정. 스마트폰 등 HMI
Fingerprint Imager (지문센서) 지문의 요철을 커패시터 센서로 인식 Fusitsu MBF200: 256x300 pixels, 500 dpi