Electrostatics: CapacitanceFrom Coulomb’s Law to charge storage

So what is capacitance?Capacitance is basically the ability of an electric conductor to store an electric charge, and is usually defined as the total electric charge placed on the object divided by the potential of the object, C = Q / Vwith the capacitance “C” in Farads (F), the charge “Q” in Coulombs (C), and the potential “V” in Volts (V).

A capacitor is a device designed to provide capacitance in an electric circuit by supplying it with the ability to store energy in an electric field between two conducting bodies (eg. two pieces of charged metal). In its most basic form, a capacitor consists of two conducting plates separated by an insulating layer called a dielectric. When a capacitor is connected across a voltage source, such as a battery, the voltage forces electrons onto one plate resulting in a negatively charged plate. The electrons of the other plate are pulled off by the battery resulting in a positively charged plate. Because the dielectric between the plates is an insulator, current cannot flow through it and a potential difference is created between them. A capacitor has a finite amount of capacity to store charges. When a capacitor reaches its capacity it is fully charged and will not store any more charge.

http://micro.magnet.fsu.edu/electromag/electricity/capacitance.html

Electrostatics: CapacitanceFrom Coulomb’s Law to charge storage

Rabbit fur More

positive

Glass  

Human hair  

Polyamide (nylon)  

Wool  

Fur  

Silk  

Aluminum  

Paper  

Cotton  

Steel  

Wood  

Rubber  

Acetate rayon  

Polyethylene (PE) and polypropylene (PP)

 

PET  

PVC  

Polyurethane  

PTFE More negative

To the right is a list of some

everyday objects and their relative

charges.

This chart provides an easy reference to determine the ease with which rubbing materials together will transfer charge. The farther apart they are, the more readily charge is separated. Balloons are made of latex (rubber).

Capacitor battery: http://micro.magnet.fsu.edu/electromag/java/capacitor/index.htmlInductance applets: http://micro.magnet.fsu.edu/electromag/java/faraday/,

http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html

Electrostatics: CapacitanceFrom Coulomb’s Law to charge storage

chargedsurface

induced dipole in (neutral)solid conductor

_______

For a metal, charges move freely.

++++

___

_

Force

chargedsurface

induced dipole in (neutral) solid conductor

_______

++++

___

_

Force

++

+

++

_

___

_

Electrostatics: CapacitanceFrom Coulomb’s Law to charge storage

chargedsurface

induced dipole in (neutral)solid polar solution or solid

_______

For a polar material like water, charges are able to move short distances, but are localized around the ‘donating’ atom. Solid polar materials are known as dielectrics.

Force

_+

_+_+ _+_+_+_+

chargedsurface

induced dipole in (neutral)solid polar solution or solid

_______

_+_+ _+_+_+_+

Electric dipole

Force

H OH

_+

+

Electrostatics: CapacitanceThe untold story

charged metalsurface

induced dipole in (neutral)solid polar solution or solid

_______

As the neutral, polarized material gets closer to the charged surface, the charges on the charged surface redistribute (again, due to Coulomb’s forces). This behavior is called induction. For an applet, see

_+_+ _+_+_+_+

chargedsurface

induced dipole in (neutral)solid polar solution or solid

_____

_+_+ _+_+_+_+_

_

http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html

Charge by InductionCharge by induction is simply charging a neutral object by

bringing a charged conductor close to it, which manipulates electrons, but never actually making contact between the objects. Charge is not passed as with conduction, it is “induced”. This principle is illustrated in the diagram below:

Charging objectsBy means of electrical induction

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/estatics/u8l2b.html

Electrostatics: CapacitanceThe capacitor

charged metalsurface

______

A dielectric is placed between the charged plates because it helps the capacitor to accumulate more charge.

What characteristics does the optimal dielectric have?

_+_+ _+_+_+_+

charged metal

surface

______

++++++

++++++

•High ‘polarizability’•Highly insulating ability•Thermal stability•Water insolubility

Unit of measure for a capacitor is Farads, after Faraday.1 Farad = 1 Coulomb/Volt or C = q/V = 0A/d, where 0 is the permitivity constant

http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html

Charging ObjectsMethods that do NOT involve induction

Charge SeparationAll matter is composed of atoms, which are composed of

negative electrons and positive protons. These opposite charges attract each other and require a force to separate. Rubbing your feet on the carpet, combing your hair (both “charge by friction”), or passing a wire through a magnetic field can provide such a force. Once the charges are separated, they can be drawn back together in a way that the energy produced can be harnessed for something like lighting a lamp.

Charge by ConductionAlso called charging by contact, charge by conduction is

simply taking a negatively or positively charged object, touching it to a neutral object, and thus giving that neutral object a charge. This was the method used by Coulomb to charge his pith balls in his famous torsion balance experiment.

Electrostatics: CapacitanceLightning Moisture accumulates in the atmosphere

as a cloud containing millions upon millions of suspended water droplets and ice. These ice droplets collide with each other as the moisture rises. The importance of these collisions is that electrons are transferred between particles. The larger ones accumulate electrons and fall toward earth from gravity. The smaller ones have a positive potential and rise to the top of the clouds.

_ _ _

earth

+ + + + + + +

_ _ _ _ _

This mimics a capacitor. When the voltage becomes high enough, lightning strikes by ionizing the air and creating a conductive path to ground.

Lightning/capacitor: http://micro.magnet.fsu.edu/electromag/java/lightning/index.html

Electrostatics: CapacitanceLightning

                                                                            

•Voltage: 10-100 MV •Peak current: 5-20 kA •Power per stroke: P = VI = 50-2000 GW •Same website: A moderate thunderstorm generates several hundred megawatts of electrical power. FALSE (You do the math…)•The Discovery Channel in Canada put this in layman's terms, explaining that one lightning strike has enough energy to light 150,000,000 light bulbs MISLEADING •Energy: E = PT = 3.5 to 140 MJ•An Atlanta Journal article states that one storm can discharge enough energy to supply the entire U.S. with electricity for 20 minutes FALSE

Power company: One lightning strike can carry enough electricity to power 10 million homes for one month. FALSEOne 100 W light bulb operating for one month = 260 MJ

The key is understanding the duration of a bolt.

Electrodynamics: OhmThe MAN: Georg Simon Ohm

Ohm sought a connection between voltage and current. Unfortunately, Ohm's law was met with ‘resistance.’ Many of his countrymen were used to experimenting with voltage and current, but they considered these to be entirely separate phenomena.

Electrodynamics: OhmThe MAN: Charles Augustin de Coulomb

In his experiments, Ohm used thin resistive wire of various lengths in simple circuits. He found that V = IR (voltage = current × resistance). Voltage was supplied to the circuit by a thermocouple and current was measured by measuring the deflection of a thin magnet near the wire.