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Chapter 20 Magnetism Magnets • Poles of a magnet are the ends where objects are most strongly attracted – Two poles, called north and south • Like poles repel each other and unlike poles attract each other – Similar to electric charges • Magnetic poles cannot be isolated – If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole More About Magnetism • An unmagnetized piece of iron can be magnetized by stroking it with a magnet – Somewhat like stroking an object to charge an object • Magnetism can be induced – If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized Types of Magnetic Materials • Soft magnetic materials, such as iron, are easily magnetized – They also tend to lose their magnetism easily • Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize – They tend to retain their magnetism Magnetic Fields • A vector quantity • Symbolized by B • Direction is given by the direction a north pole of a compass needle points in that location • Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look 20.1 Magnets and Magnetic Fields Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract. 20.1 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. 20.1 Magnets and Magnetic Fields Magnetic fields can be visualized using magnetic field lines, which are always closed loops. Magnetic 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) Magnetic Field Lines, Bar Magnet • Iron filings are used to show the pattern of the electric field lines • The direction of the field is the direction a north pole would point Magnetic Field Lines, Unlike Poles • Iron filings are used to show the pattern of the electric field lines • The direction of the field is the direction a north pole would point – Compare to the electric field produced by an electric dipole Magnetic Field Lines, Like Poles • Iron filings are used to show the pattern of the electric field lines • The direction of the field is the direction a north pole would point – Compare to the electric field produced by like charges Domains, cont • Random alignment, a, shows an unmagnetized material • When an external field is applied, the domains aligned with B grow, b Earth’s Magnetic Field • The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior Earth’s Magnetic Declination Declination is the difference between true north and magnetic north as read by a compass Earth’s magnetic field reverses every few million years Migration patterns may be guided by Earth’s magnetic field Magnetic Fields, cont • When 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 charge – Similar to the way electric fields are defined F B qv sin Units of Magnetic Field • The SI unit of magnetic field is the Tesla (T) Wb N N T 2 m C (m / s) A m – Wb is a Weber • The cgs unit is a Gauss (G) – 1 T = 104 G Finding the Direction of Magnetic Force • Experiments show that the direction of the magnetic force is always perpendicular to both v and B • Fmax occurs when v is perpendicular to B • F = 0 when v is parallel to B Right Hand Rulefor individual charges • Hold your right hand open • Place your fingers in the direction of B • Place your thumb in the direction of v • The direction of the force on a positive charge is directed out of your palm – If the charge is negative, the force is opposite that determined by the right hand rule Force on a Wire • The blue x’s indicate the magnetic field is directed into the page • Blue dots would be used to represent the field directed out of the page • In this case, there is no current, so there is no force Right Hand Rulefor current carrying wires • Hold your right hand open • Place your fingers in the direction of B • Place your thumb in the direction of I • The direction of the force is directed out of your palm Force on a Wire • B is into the page – Point your fingers into the page • The current velocity is up the page – Point your thumb up the page • The force is to the left – Your palm should be pointing to the left Force on a Wire, final • B is into the page – Point your fingers into the page • The current is down the page – Point your thumb down the page • The force is to the right – Your palm should be pointing to the right Force on a Wire, equation • The magnetic force is exerted on each moving charge in the wire • The total force is the sum of all the magnetic forces on all the individual charges producing the current • F = B I ℓ sin θ – θ is the angle between B and I – The direction is found by the right hand rule, pointing your thumb in the direction of I instead of v 20.2 Electric Currents Produce Magnetic Fields The direction of the field is given by a right-hand rule. Electric Motor • An electric motor converts electrical energy to mechanical energy – The mechanical energy is in the form of rotational kinetic energy • An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field Torque on a Current Loop T = NBIAsinθ – Applies to any shape loop – N is the number of turns in the coil Force 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 field • The force is always directed toward the center of the circular path • The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle Force on a Charged Particle • Equating the magnetic and centripetal forces: mv 2 F qvB r mv • Solving for r: r qB – r is proportional to the momentum of the particle and inversely proportional to the magnetic field Bending an Electron Beam in an External Magnetic Field Particle 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 spiral – The spiral path is called a helix Magnetic Fields – Long Straight Wire • A current-carrying wire produces a magnetic field • The compass needle deflects in directions tangent to the circle – The compass needle points in the direction of the magnetic field produced by the current Direction of the Field of a Long Straight Wire • Right Hand Rule #2 – Grasp the wire in your right hand – Point your thumb in the direction of the current – Your fingers will curl in the direction of the field Magnitude 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 is oI B 2r • µo = 4 x 10-7 T m / A – µo is called the permeability of free space • Equation for B is derived using Ampere’s Law Magnetic 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 2 • The force per unit length is: F o I1 I2 2d Force Between Two Conductors, cont • Parallel conductors carrying currents in the same direction attract each other • Parallel conductors carrying currents in the opposite directions repel each other Magnetic Field of a Current Loop – Total Field Magnetic 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 solenoid • It is also known as an electromagnet since it acts like a magnet only when it carries a current 20.5 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: 20.6 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) 20.6 Force between Two Parallel Wires Parallel currents attract; antiparallel currents repel. 20.7 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) 20.7 Solenoids and Electromagnets If a piece of iron is inserted in the solenoid, the magnetic field greatly increases. Such electromagnets have many practical applications. 20.10 Applications: Galvanometers, Motors, Loudspeakers A galvanometer takes advantage of the torque on a current loop to measure current. 20.10 Applications: Galvanometers, Motors, Loudspeakers An electric motor also takes advantage of the torque on a current loop, to change electrical energy to mechanical energy. 20.10 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. 20.3 Force on an Electric Current in a Magnetic Field; Definition of B A magnet exerts a force on a currentcarrying wire. The direction of the force is given by a right-hand rule. 20.11 Mass Spectrometer A 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: 20.11 Mass Spectrometer All the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass. Summary of Chapter 20 • Magnets have north and south poles • Like poles repel, unlike attract • Unit of magnetic field: tesla • Electric currents produce magnetic fields • A magnetic field exerts a force on an electric current: Summary of Chapter 20 • A 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 Summary of Chapter 20 • Magnetic field inside a solenoid: • Ampère’s law: • Torque on a current loop: