Chapter6ElectromagneticInductionLaw ofElectromagnetic InductionInductancesEnergy and Force1.Law of ElectromagneticInduction2.Inductances3. Energy in Steady Magnetic Fields4. Magnetic Forces
Chapter 6 Electromagnetic Induction Law of Electromagnetic Induction Inductances Energy and Force 1. Law of Electromagnetic Induction 2. Inductances 3. Energy in Steady Magnetic Fields 4. Magnetic Forces
1.LawofElectromagneticInductionFrom physics we know that when the magnetic flux @through aclosed coil is changing, an induced electromotiveforce e willbegenerated in the coil, with the relationdddtwhere the positive direction of the electromotive force e and that of themagnetic flux comply with theleft hand rule.If the magnetic flux is increased with time, the direction of theinduced electromotiveforceand that of the magnetic flux obeythe lefthand rule ifthe magnetic flux is decreased with time, they will obey theright handrule
1. Law of Electromagnetic Induction From physics we know that when the magnetic flux through a closed coil is changing, an induced electromotive force e will be generated in the coil, with the relation t e d d = − where the positive direction of the electromotive force e and that of the magnetic flux comply with the left hand rule. If the magnetic flux is increased with time, the direction of the induced electromotive force and that of the magnetic flux obey the left hand rule. if the magnetic flux is decreased with time, they will obey the right hand rule
The induced magnetic flux caused by theinduced current in the coil always resists thechange of the original magnetic flux. Theinduced magnetic flux is called the reactionmagnetic flux, and the induced electromotiveforceis called the backelectromotiveforce.When the induced electromotiveforceis generated in the coil.there is an electric field to push the charges to move in the coil, andthis induced electricfieldis denoted as EThe lineintegral of theinduced electricfield intensityaroundthe closed coil is equal to the induced electromotiveforcein the coile, i.e.d@fE-dl=e -dtUV
e I The induced magnetic flux caused by the induced current in the coil always resists the change of the original magnetic flux. The induced magnetic flux is called the reaction magnetic flux, and the induced electromotive force is called the back electromotive force. When the induced electromotive force is generated in the coil, there is an electric field to push the charges to move in the coil, and this induced electric field is denoted as E. t e l d d d = = − E l The line integral of the induced electric field intensity around the closed coil is equal to the induced electromotive force in the coil e, i.e
Considering @= [B.ds, we havefedl--%[B.dsatWhichis called the lawof electromagneticinduction,and it shows thatwhen the magnetic field through a closed coilis changing, an inducedelectric field will be generated in the coilThe law of electromagnetic induction shows that a time-varyingmagnetic field can produce a time-variableelectric fieldBased on Stokes'theorem, fromthe above eguation we haveaB(V×E)+dS = 0atSince the equation holds for any area S, the integrand must bezero, so thataBVxE=atUEV
Considering , we have = S B dS = − l S t E dl B dS Which is called the law of electromagnetic induction, and it shows that when the magnetic field through a closed coil is changing, an induced electric field will be generated in the coil. The law of electromagnetic induction shows that a time-varying magnetic field can produce a time-variable electric field. Based on Stokes’ theorem, from the above equation we have ( ) d 0 = + S B E S t Since the equation holds for any area S, the integrand must be zero, so that t = − B E
aBVxE-atwhich is called the differential form of law of electromagneticinduction, and it means that the negative time rate of change ofthe magnetic flux density at a point is equal to the curl of the timevariableelectricfieldintensityatthatpointThe law of electromagnetic induction is one of basic laws fortime-varying electromagnetic fields, and it is also one of Maxwell'sequations.U7
which is called the differential form of law of electromagnetic induction, and it means that the negative time rate of change of the magnetic flux density at a point is equal to the curl of the timevariable electric field intensity at that point. The law of electromagnetic induction is one of basic laws for time-varying electromagnetic fields, and it is also one of Maxwell’s equations. t = − B E