physics lecture notes (applications of electric fields 2011)€¦ · 1 volt = 1 joule coulomb -...
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Lecture Notes (Applications Of Electric Fields)
Electric Potential Energy: - an object has a gravitational energy because of its location in a gravitational field; likewise, a charged object has potential energy by virtue of its location in an electric field - just as work is required to lift a massive object against the gravitational field of the Earth, work is also required to push a charged particle against the electric field of a charged body - this work will change the electric potential energy of the charged particle; the work will be positive if it increases the electric potential energy of the charged particle and negative if it decreases the electric potential energy of the charged particle - the energy a particle possesses by virtue of its position is its electric potential energy - upon being released, a charge may accelerate towards or away from the field charge and its electric potential energy will change into kinetic energy - if we were to push a particle with twice the charge instead, we would do twice as much work pushing it; so the doubly charged particle in the same location has twice as much electric potential energy as before
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Electric Potential: - we will use another term to help simplify electric potential energy problems; this term is electric potential; which is the amount of electric potential energy per charge:
electric potential energyelectric potentialcharge
; eUVq
- the unit of measurement for electric potential is the volt (V); 1 volt = 1 joule coulomb - electric potential and voltage are the same thing; one speaks of the potential (or voltage) at a particular point in space; charges do not have potential
Electric Potential Difference: - electric potential difference is the change in electric potential;
final initialV V V
- V is defined as the work done moving a test charge in an electric field divided by the magnitude of the test charge
( ) on qW
qV =
- V is measured in volts (V)
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How dangerous is 5000 volts? - as one million electrons are added to a neutral balloon, its potential rises from zero to 5000 volts; because there aren't many coulombs at high voltage, there is too little energy to do any harm. - voltage is analogous to water pressure difference
- the electrons on the balloon question were at a high "electrical pressure", or voltage; but that pressure quickly fell once most of the electrons flew off the balloon; if the charges were constantly replaced as the electrons passed into a person, then the balloon would give a serious shock - lets take a look at the changes in V when we move the location of a positive test charge relative to a negative field charge
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- remember, if you the force applied to the test charge raises its electric potential energy Ue, then the work done on the charge is positive - conversely, if the force applied to the test charge lowers Ue, then W is negative - only differences in electric potential can be measured; these differences are measured with a voltmeter - the electric potential of any point can be defined as zero; no matter what reference point is chosen, the potential difference between those two points is the same - below is a diagram which displays changes in electric potential Equipotential: - a surface upon which all points are the same potential is called an equipotential surface - the potential difference V between any two points on an equipotential surface is zero - no work is required to move a charge at constant speed on an equipotential surface
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- the electric field, E, is perpendicular to the surface at every point on an equipotential surface - equipotential contours are drawn on diagrams to represent equipotential surfaces
Uniform Fields: - you can create situations where the electric force and field are uniform by placing two large flat conducting plates parallel to one another - one plate is positively charged and the other is negatively charged - the field between the plates is constant except at the edges of the plates
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- for uniform fields the potential difference (ΔV) between two points A and B a distance, d, apart in a uniform field, E, is represented as:
ΔV = Ed
Millikan's Oil-Drop Experiment: - this experiment was conducted by Robert Millikan in 1909; his goal was to find the charge of an electron - Millikan used two parallel plates to form a uniform electric field - he sprayed tiny oil drops from an atomizer; the atomizer charged the oil drops by friction; gravity caused the drops to fall and a few drops would fall through a hole in the top charged plate - a potential difference was set up between the plates which caused an electric field to form - this field exerted enough force on the oil drop to cause it to rise and become suspended in air
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- this allowed Millikan to find the electron's charge by calculating the field strength and the mass of the oil drop - his data showed that the charge is quantized; an object can only have a charge with a magnitude that is some multiple of the fundamental charge of an electron Sharing of Charge: - a system will reach a state of equilibrium when its energy is at a minimum; for example, if you set a bowling ball on a hill it will roll down the hill and come to rest at the lowest point - this lowers the gravitational potential energy, Ug, of the ball - this same principle works with how charges distribute themselves on the surface of insulating objects
Charge on Metals Charge on Insulators Charge on Points
Metal Ball Plastic Ball Lightning Rod
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- like charges repel each other, so they will spread out from each other on the surface of an insulator; this will decrease the amount of electric potential energy, Ue - if we touch a neutral object to a charged one, the charge will spread from the charged object to the neutral object
- the size (amount of surface area) is an important factor in sharing charge; the larger the object, the more charge it can hold as equilibrium is reached
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- this can also be stated as, the charge will move to the object with the lower potential difference until there is no electric potential difference between the objects - this phenomenon also holds true for conductors; charges will distribute themselves along the surface equally - the surface of a conductor has no potential difference and is therefore an equipotential surface Fields Near Conductors: - on solid conductors, all charges migrate to the surface - on hollow conductors, all charges orient themselves on the outer surface (this phenomenon is what protects people in cars when lightning strikes) - electric fields on the outside of a conductor are affected by the shape of the object - as the shape of the object becomes more pointed, the field will intensify - if the field becomes strong enough, it can separate electrons from air molecules; as the electrons combine with other positive ions, light is produced creating a corona glow
A corona discharge from an electrical wire.
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- if the field is stronger still, the electrons that are stripped will have enough energy to separate more electrons causing a stream of ions called plasma
- plasma is a conductor which will result in a spark or lightning Lightning Arrestors: - during thunderstorms clouds build up very large potentials due to charge separation within the cloud; this effect induces a large build-up of charge onto buildings and objects rising up from the ground, which could act as discharge points or points for lightning to strike - lightning arrestors are a series of upwardly pointing metal rods or spikes, are connected to a copper grounding wire that runs down the building to the earth
A 4' plasma tower displaying a series of plasma streams.
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- this system allows rapid discharge to the air of charge built up at the top of the building and thus helps to prevent lightning strikes
Capacitors: - in 1746, a Dutch physician/physicist created a device which stored electric charge; his name was Pieter van Musschenbroek and the device was called a Leyden jar (named after the city in which Musschenbroek lived) - the Leyden jar was the simplest form of capacitor (a device which stores charge); its design consists of a narrow- necked glass jar coated over part of its inner and outer surfaces with conductive metal foil; a conducting rod or wire
Leyden Jar
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passes through an insulating stopper in the neck of the jar and contacts the inner foil layer, which is separated from the outer layer by the glass wall - by modern standards, the Leyden jar is cumbersome and inefficient; it is rarely used except in laboratory demonstrations of capacitance - the modern day capacitor is used in a variety of electric circuits - the basic design of a capacitor is a series of parallel metal plates separated by some distance; the plates are connected to the positive and negative terminals of a battery or other voltage source
- when a connection is made, electrons from one plate are stripped off and transferred to the other plate - this process stops when the potential difference across the plates equals that of the battery or other voltage source - thus, the charged capacitor is a device that stores energy which can be reclaimed when needed for a specific application - the two plates are conductors, the space between them is an insulator such as air or plastic
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- the capacitance (C) of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference (ΔV) between the conductors (plates)
qCV
- capacitance is measured in farads (F); where one farad is one coulomb per volt - one farad is a lot of capacitance; capacitors usually have a capacitance between 10 picofarads - 500 microfarads