1. Chapter 19 Magnetism

2. General Physics Review – Magnetic Fields ELECTRIC FIELDS From (+) to (–) charges Field lines (electric flux) Start / End at charges NO loops! (cons. energy) Force Law: F = q E (does work)  = d × E (elec. dipole) MAGNETIC FIELDS From (N) to (S) poles Field lines (magnetic flux) NO monopoles! (Start/End) Loop (S) to (N) inside Force Law: ( × = sin  ) F = q v × B (deflection) F = B I L (wire)  =  × B (mag. dipole)

3. General Physics Review – Right-hand rule Essence of a cross product Essence of a cross product F = q v × B v B sin  F = q v × B v B sin  Force is perpendicular to both velocity and field Force is perpendicular to both velocity and field Need right-hand rule to decide which direction Need right-hand rule to decide which direction Deflection doesn’t do work Deflection doesn’t do work

4. General Physics Magnetic Fields II Sections 6–10

5. General Physics Motion of a Charged Particle in a Uniform 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

6. General Physics Equating the magnetic and centripetal forces: Solving for the radius r: r is proportional to the momentum mv of the particle and inversely proportional to the magnetic field Sometimes called the cyclotron equation Motion of a Charged Particle in a Uniform Magnetic Field, cont Active Figure: Motion of a Charged Particle in a Uniform Magnetic FieldMotion of a Charged Particle in a Uniform Magnetic Field

7. General Physics The Mass Spectrometer: Separating Isotopes The cyclotron equation can be applied to the process of separating isotopes Singly ionized isotopes are injected into a velocity selector Only those isotopes with velocity v = E/B pass into the deflection chamber—Why? Isotopes travel in different circular paths governed by the cyclotron equation—therefore different mass isotopes separate Active Figure: The Mass SpectrometerThe Mass Spectrometer

8. General Physics Magnetic Spectrometer with Drift (Ion) Chambers 2 sectors × 3 drift chambers 2 sectors × 3 drift chambers 954 sense wires 954 sense wires resolution 200 μm resolution 200 μm signal to noise 20:1 signal to noise 20:1 8-coil toroid electromagnet 8-coil toroid electromagnet 0.3 T maximum field 0.3 T maximum field

9. General Physics Particle Moving in an External Magnetic Field If the particle’s velocity is not perpendicular to the magnetic field, the path followed by the particle is a spiral The spiral path is called a helix Active Figure: A Charged Particle with a Helical PathA Charged Particle with a Helical Path

10. General Physics Charged Particles Trapped in the Earth’s Magnetic Field—Auroras Charged particles from the Sun enter the Earth’s magnetic field These particles move in spirals around the lines of magnetic field This causes them to become trapped in the Earth’s magnetic field An aurora is caused by these trapped charged particles colliding with atoms in the upper atmosphere—producing beautiful displays of light

11. General Physics Charged Particles Trapped in the Earth’s Magnetic Field—Auroras

12. General Physics Charged Particles Trapped in the Earth’s Magnetic Field—Auroras

13. General Physics Charged Particles Trapped in the Earth’s Magnetic Field—Auroras

14. General Physics Hans Christian Oersted 1777 – 1851 Best known for observing that a compass needle deflects when placed near a wire carrying a current First evidence of a connection between electric and magnetic phenomena

15. General Physics 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 Active Figure: Magnetic Field Due to a Long Straight WireMagnetic Field Due to a Long Straight Wire

16. General Physics 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

17. General Physics 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 µ o = 4  x 10 -7 T. m / A µ o is called the permeability of free space

18. General Physics André-Marie Ampère 1775 – 1836 Credited with the discovery of electromagnetism Relationship between electric currents and magnetic fields Mathematical genius evident by age 12

19. General Physics Ampère’s Law André-Marie Ampère found a procedure for deriving the relationship between the current in a wire and the magnetic field produced by the wire Ampère’s Circuital Law  B || Δℓ = µ o I Sum over the closed path around the current I Choose an arbitrary closed path around the current Sum all the products of B || Δℓ around the closed path

20. General Physics Ampère’s Law to Find B for a Long Straight Wire Sum over a closed circular path around current I  B || Δℓ = µ o I Sum all products B || Δℓ around the closed path B·2  r = µ o I The magnitude of the magnetic field a distance r from the wire

21. General Physics Magnetic Field of a Current Loop The strength of a magnetic field produced by a wire can be enhanced by forming the wire into a loop All the segments, Δx, contribute to the field, increasing its strength The magnitude of the magnetic field at the center of a circular loop with a radius R

22. General Physics Magnetic Field of a Current Loop – Total Field

23. General Physics 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

24. General Physics Magnetic Field of a Solenoid, 2 The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together This indicates that the field inside the solenoid is nearly uniform and strong The exterior field is nonuniform, much weaker, and in the opposite direction to the field inside the solenoid

25. General Physics Magnetic Field in a Solenoid, 3 The field lines of the solenoid resemble those of a bar magnet – dipole magnetic field

26. General Physics Magnetic Field in a Solenoid from Ampère’s Law A cross-sectional view of a tightly wound solenoid If the solenoid is long compared to its radius, we assume the field inside is uniform and outside is zero Apply Ampère’s Law to the blue dashed rectangle The magnitude of the field inside a solenoid is constant at all points far from its ends n is the number of turns per unit length n = N / ℓ

27. General Physics 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:

28. General Physics 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 Active Figure: Force Between Long Parallel WiresForce Between Long Parallel Wires

29. General Physics Defining Ampere and Coulomb The force between parallel conductors can be used to define the Ampere (A) If two long, parallel wires 1 m apart carry the same current, and the magnitude of the magnetic force per unit length is 2 x 10 -7 N/m, then the current is defined to be 1 A The SI unit of charge, the Coulomb (C), can be defined in terms of the Ampere If a conductor carries a steady current of 1 A, then the quantity of charge that flows through any cross section in 1 second is 1 C

30. General Physics Magnetic Effects of Electrons – Orbits An individual atom should act like a magnet because of the motion of the electrons about the nucleus Each electron circles the atom once in about every 10 -16 seconds This would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular path However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom The net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials

31. General Physics Magnetic Effects of Electrons – Spins Electrons also have spin The classical model is to consider the electrons to spin like tops It is actually a quantum effect

32. General Physics Magnetic Effects of Electrons – Spins, cont The field due to the spinning is generally stronger than the field due to the orbital motion Electrons usually pair up with their spins opposite each other, so their fields cancel each other That is why most materials are not naturally magnetic

33. General Physics Magnetic Effects of Electrons – Domains In some materials, the spins do not naturally cancel Such materials are called ferromagnetic Large groups of atoms in which the spins are aligned are called domains When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become magnetized

34. General Physics Domains, cont Random alignment (left) shows an unmagnetized material When an external field is applied, the domains aligned with B grow (right)

35. General Physics Domains and Permanent Magnets In hard magnetic materials, the domains remain aligned after the external field is removed The result is a permanent magnet In soft magnetic materials, once the external field is removed, thermal agitation causes the materials to quickly return to an unmagnetized state When a ferromagnetic core is placed inside a current-carrying loop, the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field