Presentation on theme: "We have looked at the magnetic field from a single loop of wire"— Presentation transcript:
1We have looked at the magnetic field from a single loop of wire We have looked at the magnetic field from a single loop of wire. It is also necessary to examine the magnetic field from a stack of looped coils. This stack is really just a wire wound into a helical shape. This configuration of looped wire is called a solenoid.The concentration of magnetic field lines is greater in the center of the solenoid, than it is outside the solenoid. This means that there will be a larger net magnetic field inside the solenoid than outside.The magnetic field for a solenoid resembles that of a bar magnet.The magnetic field will be different if the loops are closely spaced as compared to widely separated loops.The solenoid is the most commonly discussed and used loop configuration. A solenoid bent into a circle is called a toroid.
2We can use Ampere’s law to determine the magnitude of the magnetic field inside an ideal solenoid. (Assume B = 0 outside solenoid)1234Magnetic field at the center of an ideal solenoidThis equation is only valid at the center of a solenoid assuming that there is no magnetic field outside the solenoid and the coils are closely spaced.
3A solenoid has a magnetic field that through its center, which means that it passes through an area defined by the geometry of the loops. This means that there is a Magnetic Flux through the solenoid.Magnetic Flux – The amount of magnetic field that passes through a specified area.FB – Magnetic flux [Wb]B – Magnetic field strength [T]A – Area magnetic field passes through [m2]Wb – Weber = Tm2The magnetic flux is similar to the electric flux that we discussed for electric fields.Closed SurfaceThe same number of magnetic field lines enter the closed surface as leave.The net flux through a closed surface must always be zero!Electric field lines all leave the positive charge. There is a net electric flux out of the surface.Gauss’s Law of Magnetism
4A sphere of radius R is placed near a long, straight wire that carries a steady current I. The magnetic field generated by the current is B. The total magnetic flux passing throughthe sphere is1. moI.2. moI /(4pR2).3. 4pR2moI.4. zero.5. need more informationAnswer: 4. Because magnetic field lines close on themselves, the totalmagnetic flux through any closed surface is zero.
5Ampere’s Law is only valid when the electric field is constant in time Ampere’s Law is only valid when the electric field is constant in time. Time-varying electric fields are a common occurrence though and must be discussed. When a time-varying electric field is present Ampere’s Law will still be valid if we include a correction term to account for the time-varying electric field.Constant electric field - electric field from a power supply pushing charges in a single direction.Time-varying electric field – Electric field generated by a charging or discharging capacitorThe time-varying component of the electric field causes a secondary current called the displacement current.Id – displacement currentThe corrected form of Ampere’s Law becomes:Ampere – Maxwell LawThis is one of the fundamental electromagnetic equations!
6Types of Magnetic Materials Magnetic fields are created through the motion of chargesElectron orbiting nucleusRotation of electron about its own axis – called “Spin”Magnetic moments for each of these cases are inversely proportional to mass.Magnetic moment due to orbitMagnetic moment due to spinh – Planck’s ConstantMagnetization – magnetic state of a substanceB – Magnetic flux density or magnetic inductionBM - Magnetic Intensity due to magnetizationH – Magnetic Field StrengthExternal magnetic fieldc – Magnetic Susceptibility – how easy it is to magnetize a substancemm – Magnetic Permeability – how easily a magnetic field interacts with a substance
7Classes of Magnetic Materials Ferromagnetic – Crystalline substances with strong magnetic effectsUsed to make permanent magnetsStrong interaction between magnetic momentsExamples: Fe, Co and NiParamagnetic – weak magnetic effectsUsed to make permanent magnetsWeak interaction between magnetic momentsAn external magnetic field is required to align magnetic domainsc is positiveDiamagnetic – non-magnetic materialsNo permanent magnetsWeak anti-alignment when external field is applied – causes repulsionAll substances have some diamagnetic properties, but they are not observable if ferromagnetic or paramagnetic properties exist.