EXAM 1, September 22, Thursday Ch.21-23, Lectures Finding E(x,y,z) or E(r) using a) E of a point charge and superposition principle, b) or Gauss’s law c) or 2. Finding a force a) b) or

3. Finding potential using a) b) or potential of a point charge and superposition principle 4) Finding the work and potential energy

Preparation for Exam 1. Look in advance at the formula sheet on the website of the course 2. Problems worked out in Lecture notes 3. Previous midterm exams on my website 4. WebCT and assigned homework

At the Exam You’ll get 3 problems+ formula sheet Ask me the questions if you do not understand the formulation of the problem Start with the figure Get a general (algebraic) solution Indicate the units Get numerical results if required (bring your calculator)

Lectures 7 (Ch. 24) Capacitance and capacitors 1. Definitions and functions 2. Types of capacitors 3. Effective capacitance (capacitors in series and parallel) 4. Dielectrics 5. Energy stored in capacitor

Capacitor is a device to store the charge and energy. It consists of two conductors (+Q,-Q), separated by a dielectric. Store Q and V in order 1.To use it on demand (camera flash, energy back up,…) 2.To block surges of Q and V protecting sensitive devices 3.Part of tuner of a radio, selecting specific frequency of radio waves 4.Binary code of a memory Capacitance: does not depend neither on Q no on V. It is defined by the geometrical sizes and by a dielctric inside

Types of capacitors 1. II plate capacitor

Spherical capacitor ab

Cylindrical capacitor a b

SI unit of C [C]=[Q]/[V]=1C/1V=1F(farad) Symbol: Typically C~1pF-1 Michael Faradey ( ) F A=? ! Supercapacitors: C~1F-1kF 2. Electrolyte (EL) as 1 of 2 conductors oxide layer with an effective d~1nm EL 1. Using porous conductors (carbon) to increase an effective A EL d

Commercial capacitors

Capacitors in parallel: C=C 1 +C 2

Capacitors in series:

Capacitors networks Example 1. Example 2. You have 3 capacitors with capacitances 5 nF, 2nF and 2nF. Your circuit needs 6 nF. What do you do?

Capacitors networks Example 1. Example 2. You have 3 capacitors with capacitances 5 nF, 2nF and 2nF. Your circuit needs 6 nF. What do you do? 2nF 5 nF 2nF

Dielectrics different from vacuum or air are typically used in capacitors to increase the capacitance: C=KC 0, K>1 to improve a mechanical stability (avoid touching between conducting plates) to increase the dielectric strength compared to air (for air: E cr =3MV/m) Polarization of dielectric in E

Suppose capacitor was charged, σ is the surface charge density, Then a battery was removed and a dielectric was inserted. Polarization of dielectric led to induced charge on the plates,σ i, reducing E between plates: K≥1 is a dielectric constant, ε=Kε 0 is a dielectric permittivity

Suppose capacitor is connected to a battery with voltage, V. Then a dielectric is inserted. v

!

For charges interacting in a dielectric medium Coulomb’s Law Gauss’s Law Q q

Potentical energy stored in the capacitor dq -qq V Density of Energy E U can be viewed as energy stored in E inside capacitor

Insert dielectric, C=KC 0 Does U ↑or↓? 1. Charged Capacitor. Battery is removed. Then a dielectric is inserted. Q-Q dl FF

2. Capacitor is connected to battery with V=const. Then a dielectric is inserted V Energy is supplied by the battery, increasing the charge on the plates and keeping V=const

Find 1)Charge and energy of the 1 st capacitor before the switch was closed. 2) Charge of each capacitor, voltage and total energy after closing the switch.

Example Data: C 1 = C 2 = C 3 = C 4 =C=4F; V ab =28V Find: Q 1, Q 2, Q 3,Q 4, V 1, V 2, V 3,V 4