Chapter 4 Steady Electric CurrentsElectriccurrent,ElectromotiveforcePrincipleofcurrentcontinuity,Energy dissipation1. Current & Current Density2.Electromotive Force3.Principle of Current Continuity4.Boundary Conditionsfor Steady Electric Currents5.EnergyDissipationinSteadyElectricCurrentFields6.ElectrostaticSimulation
Chapter 4 Steady Electric Currents Electric current, Electromotive force Principle of current continuity, Energy dissipation. 1. Current & Current Density 2. Electromotive Force 3. Principle of Current Continuity 4. Boundary Conditions for Steady Electric Currents 5. Energy Dissipation in Steady Electric Current Fields 6. Electrostatic Simulation
1.Current&CurrentDensityClassification:Conduction current and convention currentThe conduction currentis formed by the free electrons(or holes)in a conductoror theionsin an electrolyteThe convectioncurrentis resultingfromthe motion oftheelectron, the ions, or the other charged particlesin vacuum, asolid,a liquid ora gas
1. Current & Current Density Classification: Conduction current and convention current. The conduction current is formed by the free electrons (or holes) in a conductor or the ions in an electrolyte. The convection current is resulting from the motion of the electron, the ions, or the other charged particles in vacuum, a solid, a liquid or a gas
The amount of charge flowing across a given area per unit timeis called the electric currentintensity or electric current, and it isdenoted byI. The unit of electric current is ampere (A)The relationship between electric current I and electric chargeqisdqdtThe current density is a vector, and it is denoted as J. Thedirection ofthe current densityis the same as the flowing directionof the positive charges, and the magnitude is the amount of chargethrough unit cross-sectional area per unit time.The relationshipbetween the current element dl across a directedsurface element dS and the current densityJisdI = J.dsUV
The amount of charge flowing across a given area per unit time is called the electric current intensityor electric current, and it is denoted by I. The unit of electric current is ampere (A) The relationship between electric current I and electric charge q is t q I d d = The current density is a vector, and it is denoted as J. The direction of the current density is the same as the flowing direction of the positive charges, and the magnitude is the amount of charge through unit cross-sectional area per unit time. The relationship between the current element dI across a directed surface element dS and the current density J is dI = J dS
The electric current across the area SisI =[J.dsWhich states that the electric current across an area is the flux of thecurrentdensitythrough the area.In most conducting media, the conduction current density J at apoint is proportional to the electric field intensity E at that point so thatJ=oEwhere is called the conductivity, andits unit is S/m. A largeOmeans that the conducting ability of the medium is strongerThe above equation is called the differential form of thefollowingOhm'slawU=IRUV
The electric current acrossthe area S is = S I J dS Which states that the electric current across an area is the flux of the current density through the area. In most conducting media, the conduction current density J at a point is proportional to the electric field intensityE at that pointso that J =E where is called the conductivity, and its unit is S/m. A large means that the conducting ability of the medium is stronger. The above equation is called the differential form of the followingOhm’s law U = IR
A conductorwith infinite is calleda perfect electric conductoror p.e.c..In aperfect electricconductor,electriccurrentcan beproducedwithout the influence of an electric fieldThere is no steady electric fieldin a perfect electric conductor.Otherwise, an infinite current will be generated, and it resultsin aninfiniteenergyAmedium without any conductivityis called a perfect dielectricoraninsulatorIn nature there exists no any p.e.c. or perfect dielectric
A conductor with infinite is called a perfect electric conductor, or p.e.c. A medium without any conductivity is called a perfect dielectric or an insulator. In a perfect electric conductor, electric current can be produced without the influence of an electric field. There is no steady electric field in a perfect electric conductor. Otherwise, an infinite current will be generated, and it results in an infinite energy. In nature there exists no any p.e.c. or perfect dielectric
The conductivities of several mediaunit in S/mMediaMediaConductivitiesConductivities46.17 ×107SilverSea water5.80×10710-3CopperPure water4.10×10710~5GoldDry soilTransformer3.54 ×10710-11Aluminumoil1.57×10710-12BrassGlass10710-15IronRubberu7
The conductivities of several media unit in S/m Media Conductivities Media Conductivities Silver Sea water Copper Pure water Gold Dry soil Aluminum Transformer oil Brass Glass Iron Rubber 7 6.17 107 5.80 10 3 10 − 7 4.10 10 5 10 − 7 3.54 10 11 10 − 7 1.57 10 12 10 − 7 10 15 10 − 4
The magnitude of the current density of the convection currentisnot proportional to the electric field intensity, and the direction maybe different from that of electric fieldintensityIf the charge densityis p, and the moving velocityis y, and thenJ=pvAs the polarization of dielectrics,the conducting properties of amedium can be homogeneous or inhomogeneous, linear or nonlinearand isotropic or anisotropic, with same meanings as before.The above equations are valid only fora linearisotropicmediumU
The magnitude of the current density of the convection current is not proportionalto the electric field intensity, and the direction may be different from that of electric field intensity. J = v As the polarization of dielectrics, the conducting properties of a medium can be homogeneous or inhomogeneous, linearor nonlinear, and isotropic or anisotropic, with same meanings as before. If the charge density is , and the moving velocity is v, and then The above equations are valid only for a linear isotropic medium
2.ElectromotiveForceWe first discuss the chemical action inside the impressed sourceunder open-circuitconditionIn theimpressed source,under theinfluenceofnon-electrostaticforcethepositivecharges will be moved continuouslytothepositiveelectrodeplateP,whilethenegative charges to the negative electrode7plate N.These charges on the plates produceanelectricfield E, with thedirectionpointedtoImpressed sourcethe plate N from the plateP, and theelectricfield Ewill be strongerwiththeincrease of the charges on the plates.uaV
E Conducting medium 2. Electromotive Force We first discuss the chemical action inside the impressed source under open-circuit condition. In the impressed source , under the influence of non-electrostatic force the positive charges will be moved continuously to the positive electrode plate P, while the negative charges to the negative electrode plate N. These charges on the plates produce an electric field E, with the direction pointed to the plate N from the plate P, and the electric field E will be stronger with the increase of the charges on the plates. P N E Impressed source E
The electric force caused by the charges on the plates will resistthe movement of the charges in the source. When the electric forceis equalto the non-electrostatic force,the charges are stopped, andthecharges onthe plateswill be constantSince the non-electrostatic force behaves as the force actingon the charge,the non-electrostatic forceis usually consideredas that produced by an impressedelectric fieldThis impressed electric field intensityis still defined as theforce acting on unit positive charge, but it is denoted as E
The electric force caused by the charges on the plates will resist the movement of the charges in the source. When the electric force is equal to the non-electrostatic force, the charges are stopped, and the charges on the plates will be constant. This impressed electric field intensity is still defined as the force acting on unit positive charge, but it is denoted as E'. Since the non-electrostatic force behaves as the force acting on the charge, the non-electrostatic force is usually considered as that produced by an impressed electric field
The impressed electric field E'pushes the positivecharges to thepositive electrode plate, and the negative charges to the negativeelectrodeplate,and the directionofis oppositetothat of the electricfield E produced by the charges on the plates.when the impressed electric field is equal but opposite to theelectric field produced by the charges on the plates, and the chargeswill beatrestIf the conducting medium is connected, the positive charges onthe positiveelectricplate will bemoved to the negativeelectricplatethrough the conducting medium, while the negative charges on thenegativeelectricplateto the positiveelectricplate.ln this way,thecharges on the plates will be decreased, and E < E'. The charges inthe sourcewill be moved again
The impressed electric field E' pushes the positive charges to the positive electrode plate, and the negative charges to the negative electrode plate, and the direction of is opposite to that of the electric field E produced by the charges on the plates. If the conducting medium is connected, the positive charges on the positive electric plate will be moved to the negative electric plate through the conducting medium, while the negative charges on the negative electric plate to the positive electric plate. In this way, the charges on the plates will be decreased, and E < E' . The charges in the source will be moved again. when the impressed electric field is equal but opposite to the electric field produced by the charges on the plates, and the charges will be at rest