Chapter5 SteadyMagneticFieldsMagnetic Flux Density,Field EquationsBoundary Conditions1. Magnetic Flux Density, Flux, and Field Lines2.Eguations for Steady Magnetic Fields in Free Space3.Vector&ScalarMagnetic Potentials4.MagnetizationofMedia5.EguationsforSteadyMagneticFieldsinAMedium6.Boundary Conditionsfor Steady Magnetic FieldsV
Chapter 5 Steady Magnetic Fields Magnetic Flux Density, Field Equations Boundary Conditions 1. Magnetic Flux Density, Flux, and Field Lines 2. Equations for Steady Magnetic Fields in Free Space 3. Vector & Scalar Magnetic Potentials 4. Magnetization of Media 5. Equations for Steady Magnetic Fields in A Medium 6. Boundary Conditions for Steady Magnetic Fields
1.MagneticFluxDensity,Flux,andFieldLinesA magnetic field exerts a force on a moving charge. Hence, theforce acting on the moving charges, the current element, or thetorque acting on a small current loop can be used to quantify themagneticfields.Experiments show that the magnetic force acting on a movingcharge is related not only to the magnitude and the speed of thecharge, but also to the direction of motion
1. Magnetic Flux Density, Flux, and Field Lines A magnetic field exerts a force on a moving charge. Hence, the force acting on the moving charges, the current element, or the torque acting on a small current loop can be used to quantify the magnetic fields. Experiments show that the magnetic force acting on a moving charge is related not only to the magnitude and the speed of the charge, but also to the direction of motion
The magnetic force will be maximum when the charge is movingalong a certain direction, and will be zero when the motionisperpendicular to it. We define the direction in which the force is zeroas the in-line direction, as shown in the following figure.Assuming the maximum forceis Fm,ifthe angle between the direction of chargeIn-linemotion and the in-line directionis α, theBDirectionforcewill beFFm sin αThe magnitude of the force F is proportional to the product ofthe magnitude of the charge g and the magnitude of the velocity yThis forceis called LorentzforceV
F B v In-line Direction The magnetic force will be maximum when the charge is moving along a certain direction, and will be zero when the motion is perpendicular to it. We define the direction in which the force is zero as the in-line direction, as shown in the following figure. Assuming the maximum force is Fm , if the angle between the direction of charge motion and the in-line direction is , the force will be Fm sin The magnitude of the force F is proportional to the product of the magnitude of the charge q and the magnitude of the velocity v. This force is called Lorentz force
We define a vector B whose magnitude is Fm with the directionbeing the in-line direction.The relationship between the vector Bthe charge g, the velocity v, and the force F isF = qv× B0In-lineWherevectorBis calledmagnetic fluxBDirectiondensity, and the unit is tesla ( T ).FLorentz force is always perpendicularto the direction of chargemotion. Consequently, the Lorenzforce can only change the directionof the charge in motion and there is no work done in this actionU7
We define a vector B whose magnitude is with the direction being the in-line direction. The relationship between the vectorB, the charge q, the velocity v, and the force F is qv Fm F = qv B Where vector B is called magnetic flux density, and the unit is tesla ( T ). Lorentz force is always perpendicularto the direction of charge motion. Consequently, the Lorenz force can only change the direction of the charge in motion and there is no work done in this action. In-line Direction F B v
The current elementis a segment of current-carrying wire.Themagnitude of the line element vector dl stands for the length of thecurrent element I, and the direction is that of the current IIfthe currentflowingin the currentelementIdlBis I,thendldq dlIdl =dg = vdqdtdtAnd the force F acting on the current element in a magnetic fieldwith magnetic fluxdensityBisF = Idl× Bif the currentis parallelto the magnetic flux density B, the force willbe zero. If it is perpendicularto B, the force is maximumThe direction of the magnetic force on a currentis always perpen-diculartothe direction ofthecurrentflowUV
The current element is a segment of current-carrying wire. The magnitude of the line element vector dl stands for the length of the current element I , and the direction is that of the current I. F B Idl If the current flowing in the current element is I,then q q t t q I d d d d d d d d v l l = l = = And the force F acting on the current element in a magnetic field with magnetic flux density B is F = Idl B if the current is parallel to the magnetic flux density B, the force will be zero. If it is perpendicularto B, the force is maximum. The direction of the magnetic force on a current is always perpendicular to the direction of the current flow