Lesson 4 Capacitance and Dielectrics Capacitance Capacitors in

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

conductor in electrostatic equilibrium Area A 1 E charge = 1

E Charged Plates d + -

PD between Plates áPotential drops Ed in going from + to - áV- is Ed lower than V+

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

Electric Field áWhat forms when we have separation of charge? áAn Electric Field +Q E -Q

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

Moving Charge áHow do we move charge? áWith an electric field áalong a conduction path

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Charge Separation áThe charge separation is maintained áby removing the conduction path áonce a charge separation has been produced

Capacitor Symbol

Battery Symbol + -

Can charge Capacitor a capacitor by Charging

áPlates are conductors Capacitance áEquipotential surfaces áLet V = P. D. (potential difference) between plates áQ (charge on plates) ~ V áThus Q = CV áC is a constant, CAPACITANCE

SI Units

Calculation of Capacitance áassume charge Q on plates ácalculate E between plates using Gauss’ Law áFrom E calculate V áThen use C = Q/V

Capacitors

Electric Field above Plates

going from positive to negative plate Calculating Capacitance in General DV = V V = - E · ds £ 0 f f ò i i E · d s ³ 0 choose path from + plate to - plate D V = - V ( PD across plates ) Thus V = ò - Eds (choose path + e 0 EA C = - ò + Eds || to electric field )

for Parallel Plates Capacitor - +

for Cylindrical Capacitor Q 2 pe 0 L = C = æ bö V ln ç ÷ è aø • a = radius of inner cylinder • b = radius of outer cylinder • L = length of cylinder

Combinations of Capacitors in equilibrium áParallel #same electric potential felt by each element áSeries #electric potential felt by the combination is theof sum of the Combination Capacitors potentials across each element Parallel

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Calculation of Effective Capacitance

Combination of Capacitors Series

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

áIf net charge inside these Gaussian surfaces is not zero áField lines pass through the surfaces áand cause charge to flow áThen we do have not equilibrium Calculation of Effective Capacitance I

Calculation of Effective Capacitance II

Is this parallel or series? = Question I

Is this parallel or series? + - Question II + -

Thus capacitors are in parallel Answer

Work done in charging capacitor + - in Charging Work. I Done q Capacitor + -

Calculation

Energy Density

Dielectrics

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Picture Polarization

Polarization Induced Electric Field

Dielectric Constant

Permitivity

Permitivity in Dielectrics

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