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Chapter 19

Chapter 19. Magnetism. Example 19.4 – page 635. A circular wire loop of radius 1m is placed in a magnetic field of magnitude 0.5T. The normal to the plane of the loop makes an angle of 30 0 with the magnetic field. The current in the loop is 2A in the direction shown in Fig 19.16a.

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Chapter 19

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  1. Chapter 19 Magnetism

  2. Example 19.4 – page 635 • A circular wire loop of radius 1m is placed in a magnetic field of magnitude 0.5T. The normal to the plane of the loop makes an angle of 300 with the magnetic field. The current in the loop is 2A in the direction shown in Fig 19.16a. • A) find the magnetic moment of the loop and the magnitude of the torque at this instant.

  3. Example 19.4 - continue • The area of the circular loop: • Magnetic moment of the loop: • Magnetic torque:

  4. Example 19.4 – cont. • B) The same current is carried by the rectangular 2m by 3m coil with three loops shown in Fig. 19.16b. Find the magnetic moment of the coil and the magnitude of the torque acting on the coil at that instant. • The area of the coil: • The magnetic moment of the coil: • Torque:

  5. 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

  6. Electric Motor, 2 • The torque acting on the loop will tend to rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0° • If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction

  7. Electric Motor, 3 • To provide continuous rotation in one direction, the current in the loop must periodically reverse • In ac motors, this reversal naturally occurs • In dc motors, a split-ring commutator and brushes are used • Actual motors would contain many current loops and commutators

  8. Electric Motor, final • Just as the loop becomes perpendicular to the magnetic field and the torque becomes 0, inertia carries the loop forward and the brushes cross the gaps in the ring, causing the current loop to reverse its direction • This provides more torque to continue the rotation • The process repeats itself

  9. 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

  10. Force 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 • Sometimes called the cyclotron equation

  11. Particle Moving in an External Magnetic Field • 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

  12. Example 19.5 – page 638 • A charged particle enters the magnetic field of a mass spectrometer at a speed of 1.79x106 m/s. It subsequently moves in a circular orbit with a radius of 16cm in a uniform magnetic field of magnitudes of 0.35T having a direction perpendicular to the particle’s velocity. • Find the particle’s mass-to-charge ratio, and identify it based on the table on page 639.

  13. Example 19.5 – cont. • V=1.79x106m/s • R=16cm=0.16m • B=0.35T • Θ=900 • -------------------------------------- • Find the particle’s mass-to-charge ratio (use table 19.6 – page 639)

  14. Example 19.5 – cont. • The cyclotron equation: • Solve the equation for m/q  the particle is tritium

  15. Example 19.6 – page 639 • Two singly ionized atoms move out of a slit at point S in Figure 19.22 and into a magnetic field of magnitude 0.1T pointing into the page. Each has a speed of 1x106m/s. The nucleus of the first atom contains one proton and has a mass of 1.67x10-27kg, while the nucleus of the second atom contains a proton and a neutron and has a mass of 3.34x10-27kg. Atoms with the same number of protons in the nucleus but different masses are called isotopes. The two isotopes here are hydrogen and deuterium. • Find their distance of the separation when they strike a photographic plate at P.

  16. Example 19.6 – cont. • Mass Spectrometer: Separating isotopes • B=0.1T • V=1.0x106m/s • m1=1.67x10-27kg - hydrogen • m2=3.34x10-27kg - deuterium ------------------------------------- • Find their distance of separation when they strike a photographic plate at P.

  17. Example 19.6 – cont. • Cyclotron equation for each atom: The separation x between the isotopes is:

  18. 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

  19. 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

  20. 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

  21. 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 • µo = 4  x 10-7 T.m / A • µo is called the permeability of free space

  22. Ampère’s Law • André-Marie Ampère found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wire • Ampère’s Circuital Law • B|| Δℓ = µo I • Sum over the closed path

  23. Ampère’s Law, cont • Choose an arbitrary closed path around the current • Sum all the products of B|| Δℓ around the closed path

  24. Ampère’s Law to Find B for a Long Straight Wire • Use a closed circular path • The circumference of the circle is 2  r • This is identical to the result previously obtained

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

  26. Example 19.7 – page 642 • A long, straight wire carries a current of 5A. At one instant, a proton, 4mm from the wire, travels at 1.5x103m/s parallel to the wire and in the same direction as the current (Fig. 19.27). • A) find the magnitude and the direction of the magnetic field created by the wire. • B) find the magnitude and the direction of the magnetic force the wire’s magnetic field exerts on the proton.

  27. Example 19.7 – cont. • The magnitude of the magnetic field 4mm from the wire: For direction of B, use right-hand rule #2.

  28. Example 19.7 – cont. • The magnetic force exerted by the wire on the proton: For direction of F, use right-hand rule #1.

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