Capacitance and Dielectrics áCapacitance áCapacitors in combination #Series #Parallel áEnergy stored in the electric field of capacitors and energy density áDielectrics áDielectric Strength Lesson 4

Field Above Conductor Field above surface of charged conductor Does not depend on thickness of conductor E  Q A  0    0

charge =  Area A E conductor in electrostatic equilibrium  A  0  E  d A  EdA A  closed cylinder   EdA A   E   A A  0    0

Charged Plates + - d E W  Fd  QEd  U   U   U    V  Ed  V   V  +Q-Q

 Potential drops Ed in going from + to -  V - is Ed lower than V + PD between Plates

 How does one make such a separation of charge?  Must move positive charge  Work is done on positive charge in producing separation Q -Q +Q F Work Done in Moving Charge

 What forms when we have separation of charge?  An Electric Field +Q -Q-Q E Electric Field

Capacitorb áThe work done on separating charges to fixed positions áis stored as potential energy áin this electric field, which can thus DO work CAPACITOR áThis arrangement is called a CAPACITOR

 How do we move charge?  With an electric field conduction path  along a conduction path Moving Charge

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 The charge separation is maintained  by removing the conduction path  once a charge separation has been produced  An electric component that does this is called A Capacitor Charge Separation

Capacitor Symbol

+ - Battery Symbol

Charging Capacitor Can charge a capacitor by connecting it to a battery

Capacitance  Plates are conductors  Equipotential surfaces  Let V = P.D. (potential difference) between plates  Q (charge on plates) ~ V (why?)  Thus Q = CV CAPACITANCE  C is a constant called CAPACITANCE

SI Units

Calculation of Capacitance  assume charge Q on plates  calculate E between plates using Gauss’ Law  From E calculate V  Then use C = Q/V

Capacitors

Electric Field above Plates

Calculating Capacitance in General going from positive to negative plate  V= V f  V i  E  d s i f   0 E  d s  0 choose path from+ plate to- plate  V = -V (PD across plates) ThusV=Eds + -  (choose path|| to electric field) C  EA  0 Eds + -  In order that

for Parallel Plates Capacitor - + C  Q V  EA  0 Eds   EA  0 Ed  A  0 d

C  Q V  2  0 L ln b a       a = radius of inner cylinder b = radius of outer cylinder L = length of cylinder for Cylindrical Capacitor

Combination of Capacitors Parallel Combinations of Capacitors in equilibrium  Parallel  same electric potential felt by each element  Series  electric potential felt by the combination is the sum of the potentials across each element

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Calculation of Effective Capacitance

Combination of Capacitors Series

Picture Net charge zero Why are the charges on the plates of equal magnitude ?

Calculation of Effective Capacitance I  If net charge inside these Gaussian surfaces is not zero  Field lines pass through the surfaces  and cause charge to flow  Then we do have not equilibrium

Calculation of Effective Capacitance II

Question I Is this parallel or series? =

Question II Is this parallel or series?

Work Done in Charging Capacitor Work done in charging capacitor I q

Calculation

Energy Density

Dielectrics

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Polarization

Induced Electric Field Polarization

Dielectric Constant

Permitivity

Permitivity in Dielectrics For conductors(not dielectrics )  For regions containing dielectrics all electrostatic equations containing  0 are replaced by  e.g. Gauss' Law  E  d A  Q  surface 

Dielectric Strength  The Dielectric Strength of a non conducting material is the value of the Electric Field that causes it to be a conductor.  When dielectric strength of air is surpassed we get lightning Dielectric Strength