Electric Potential Energy: Lecture Notes (Applications Of Electric Fields) - 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
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 energy U electric potential ; V charge q e - 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; V V V final initial - V is defined as the work done moving a test charge in an electric field divided by the magnitude of the test charge W( on q) V = q - V is measured in volts (V)
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
- remember, if you the force applied to the test charge raises its electric potential energy U e, then the work done on the charge is positive - conversely, if the force applied to the test charge lowers U e, 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
- 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
- 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
- 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
- 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, U e - 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
- 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.
- 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 A 4' plasma tower displaying a series of plasma streams. - 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
- 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 Leyden Jar which stores charge); its design consists of a narrownecked glass jar coated over part of its inner and outer surfaces with conductive metal foil; a conducting rod or wire
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
- 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) q C V - 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