2MagnetsPoles of a magnet are the ends where objects are most strongly attractedTwo poles, called north and southLike poles repel each other and unlike poles attract each otherSimilar to electric chargesMagnetic poles cannot be isolatedIf a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole
3More About MagnetismAn unmagnetized piece of iron can be magnetized by stroking it with a magnetSomewhat like stroking an object to charge an objectMagnetism can be inducedIf a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized
4Types of Magnetic Materials Soft magnetic materials, such as iron, are easily magnetizedThey also tend to lose their magnetism easilyHard magnetic materials, such as cobalt and nickel, are difficult to magnetizeThey tend to retain their magnetism
5Magnetic Fields A vector quantity Symbolized by B Direction is given by the direction a north pole of a compass needle points in that locationMagnetic field lines can be used to show how the field lines, as traced out by a compass, would look
620.1 Magnets and Magnetic Fields Magnets have two ends – poles – called north and south.Like poles repel; unlike poles attract.
720.1 Magnets and Magnetic Fields However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.
820.1 Magnets and Magnetic Fields Magnetic fields can be visualized using magnetic field lines, which are always closed loops.
9Magnetic Field Lines, sketch A compass can be used to show the direction of the magnetic field lines (a)A sketch of the magnetic field lines (b)
10Magnetic Field Lines, Bar Magnet Iron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would point
11Magnetic Field Lines, Unlike Poles Iron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointCompare to the electric field produced by an electric dipole
12Magnetic Field Lines, Like Poles Iron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointCompare to the electric field produced by like charges
13Domains, cont Random alignment, a, shows an unmagnetized material When an external field is applied, the domains aligned with B grow, b
14Earth’s Magnetic Field The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior
15Earth’s Magnetic Declination Declination is the difference between true north andmagnetic north as read by a compassEarth’s magnetic field reverses every few million yearsMigration patterns may be guided by Earth’s magnetic field
16Magnetic Fields, contWhen moving through a magnetic field, a charged particle experiences a magnetic force.One can define a magnetic field in terms of the magnetic force exerted on a test chargeSimilar to the way electric fields are defined
17Units of Magnetic Field The SI unit of magnetic field is the Tesla (T)Wb is a WeberThe cgs unit is a Gauss (G)1 T = 104 G
18Finding the Direction of Magnetic Force Experiments show that the direction of the magnetic force is always perpendicular to both v and BFmax occurs when v is perpendicular to BF = 0 when v is parallel to B
19Right Hand Rule- for individual charges Hold your right hand openPlace your fingers in the direction of BPlace your thumb in the direction of vThe direction of the force on a positive charge is directed out of your palmIf the charge is negative, the force is opposite that determined by the right hand rule
20Force on a WireThe blue x’s indicate the magnetic field is directed into the pageBlue dots would be used to represent the field directed out of the pageIn this case, there is no current, so there is no force
21Right Hand Rule- for current carrying wires Hold your right hand openPlace your fingers in the direction of BPlace your thumb in the direction of IThe direction of the force is directed out of your palm
22Force on a Wire B is into the page The current velocity is up the page Point your fingers into the pageThe current velocity is up the pagePoint your thumb up the pageThe force is to the leftYour palm should be pointing to the left
23Force on a Wire, final B is into the page The current is down the page Point your fingers into the pageThe current is down the pagePoint your thumb down the pageThe force is to the rightYour palm should be pointing to the right
24Force on a Wire, equation The magnetic force is exerted on each moving charge in the wireThe total force is the sum of all the magnetic forces on all the individual charges producing the currentF = B I ℓ sin θθ is the angle between B and IThe direction is found by the right hand rule, pointing your thumb in the direction of I instead of v
2520.2 Electric Currents Produce Magnetic Fields The direction of the field is given by a right-hand rule.
26Electric MotorAn electric motor converts electrical energy to mechanical energyThe mechanical energy is in the form of rotational kinetic energyAn electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field
27Torque on a Current Loop T = NBIAsinθApplies to any shape loopN is the number of turns in the coil
28Force on a Charged Particle in a Magnetic Field Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the fieldThe force is always directed toward the center of the circular pathThe magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle
29Force on a Charged Particle Equating the magnetic and centripetal forces:Solving for r:r is proportional to the momentum of the particle and inversely proportional to the magnetic field
30Bending an Electron Beam in an External Magnetic Field
31Particle Moving in an External Magnetic Field, 2 If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiralThe spiral path is called a helix
32Magnetic Fields – Long Straight Wire A current-carrying wire produces a magnetic fieldThe compass needle deflects in directions tangent to the circleThe compass needle points in the direction of the magnetic field produced by the current
33Direction of the Field of a Long Straight Wire Right Hand Rule #2Grasp the wire in your right handPoint your thumb in the direction of the currentYour fingers will curl in the direction of the field
34Magnitude of the Field of a Long Straight Wire The magnitude of the field at a distance r from a wire carrying a current of I isµo = 4 x 10-7 T m / Aµo is called the permeability of free spaceEquation for B is derived using Ampere’s Law
35Magnetic Force Between Two Parallel Conductors The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2The force per unit length is:
36Force Between Two Conductors, cont Parallel conductors carrying currents in the same direction attract each otherParallel conductors carrying currents in the opposite directions repel each other
38Magnetic Field of a Solenoid If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoidIt is also known as an electromagnet since it acts like a magnet only when it carries a current
3920.5 Magnetic Field Due to a Long Straight Wire The field is inversely proportional to the distance from the wire:(20-6)The constant μ0 is called the permeability of free space, and has the value:
4020.6 Force between Two Parallel Wires The magnetic field produced at the position of wire 2 due to the current in wire 1 is:The force this field exerts on a length l2 of wire 2 is:(20-7)
4120.6 Force between Two Parallel Wires Parallel currents attract; antiparallel currents repel.
4220.7 Solenoids and Electromagnets A solenoid is a long coil of wire. If it is tightly wrapped, the magnetic field in its interior is almost uniform:(20-8)
4320.7 Solenoids and Electromagnets If a piece of iron is inserted in the solenoid, the magnetic field greatly increases. Such electromagnets have many practical applications.
4420.10 Applications: Galvanometers, Motors, Loudspeakers A galvanometer takes advantage of the torque on a current loop to measure current.
4520.10 Applications: Galvanometers, Motors, Loudspeakers An electric motor also takes advantage of the torque on a current loop, to change electrical energy to mechanical energy.
4620.10 Applications: Galvanometers, Motors, Loudspeakers Loudspeakers use the principle that a magnet exerts a force on a current-carrying wire to convert electrical signals into mechanical vibrations, producing sound.
4720.3 Force on an Electric Current in a Magnetic Field; Definition of B A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.
4820.11 Mass SpectrometerA mass spectrometer measures the masses of atoms. If a charged particle is moving through perpendicular electric and magnetic fields, there is a particular speed at which it will not be deflected:
4920.11 Mass SpectrometerAll the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass.
50Summary of Chapter 20 Magnets have north and south poles Like poles repel, unlike attractUnit of magnetic field: teslaElectric currents produce magnetic fieldsA magnetic field exerts a force on an electric current:
51Summary of Chapter 20A magnetic field exerts a force on a moving charge:Magnitude of the field of a long, straight current-carrying wire:Parallel currents attract; antiparallel currents repel
52Summary of Chapter 20 Magnetic field inside a solenoid: Ampère’s law: Torque on a current loop: