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Exercise: A Complicated Resistive Circuit

A. B. D. C. Exercise: A Complicated Resistive Circuit. I 2. I 1. I 3. Loop 1. Loop 2. Loop 3. I 4. I 5. Loop 4. Find currents through resistors. loop 1:. loop 2:. loop 3:. nodes:. Five independent equations and five unknowns. Chapter 21. Magnetic Force.

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Exercise: A Complicated Resistive Circuit

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  1. A B D C

  2. Exercise: A Complicated Resistive Circuit I2 I1 I3 Loop 1 Loop 2 Loop 3 I4 I5 Loop 4 Find currents through resistors loop 1: loop 2: loop 3: nodes: Five independent equations and five unknowns

  3. Chapter 21 Magnetic Force

  4. Magnetic Field of a Moving Charge The Biot-Savart law for a moving charge The Biot-Savart law for a short piece of wire: How does magnetic field affects other charges?

  5. Magnetic Force on a Moving Charge Direction of the magnetic force depends on: the direction of B the direction of v of the moving charge the sign of the moving charge q – charge of the particle v – speed of the particle B – magnetic field

  6. Right Hand Rule for Magnetic Force Electron charge = -e: The magnetic force on a moving electron is in opposite direction to the direction of the cross product

  7. Effect of B on the Speed of the Charge What is the effect on the magnitude of speed? Kinetic energy does not change Magnetic field cannot change a particle’s energy! Magnetic field cannot change a particle’s speed! Magnetic force can only change the direction of velocity but not its magnitude

  8. Magnitude of the Magnetic Force Single electron in uniform B: (v<<c) e/me = 1.78.1011 C/kg m/s ; =(1.78.1011 C/kg)m/s)() = 5.3 m/s2 Same as acceleration due to an E= V

  9. Motion in a Magnetic Field What if we have large (infinite) area with constant Bv Confined area: deflection

  10. Circular Motion at any Speed Any rotating vector: …angular speed Cyclotron Frequency

  11. Circular Motion at Low Speed if v<<c: independent of v! Alternative derivation: Circular motion: Period T: Non-Relativistic

  12. Determining the Momentum of a Particle valid even for relativistic speeds Position vector r: Circular motion Used to measure momentum in high-energy particle experiments

  13. Determining e/m of an Electron

  14. Joseph John Thomson (1856-1940) 1897: m/e >1000 times smaller than H atom

  15. Clicker Question

  16. Clicker Question

  17. Exercise What if v is not perpendicular to B? Direction? Magnitude? Trajectory: helix

  18. Exercise: Circular Motion Which direction is electron going?

  19. The Lorentz Force Can combine electric and magnetic forces: Coulomb law and Biot-Savart law have coefficients 1/(40) and 0/(4) to make the field and force equations consistent with each other

  20. A Velocity Selector E FE FB B Is it possible to arrange E and B fields so that the total force on a moving charge is zero? What if v changes?

  21. A negative charge is placed at rest in a magnetic field as shown below. What is the direction of the magnetic force on the charge? B 73 of 140 0 • Up • Down • Into the page • Out of the page • No force at all.

  22. A negatively charged particle is moving horizontally to the right in a uniform magnetic field that is pointing in the same direction as the velocity. What is the direction of the magnetic force on the charge? 72 of 140 0 • Up • Down • Into the page • Out of the page • No force at all. B

  23. Now, another negatively charged particle is moving upward and to the right in a uniform magnetic field that points in the horizontal direction. What is the direction of the magnetic force on the charge? B 70 of 140 0 • Left • Up • Down • Into the page • Out of the page

  24. Magnetic Force on a Current-carrying Wire Current:many charges are moving Superposition: add up forces on individual charges Number of moving charges in short wire: I Total force: Force of a short wire: In metals: charges q are negative. Will this equation still work?

  25. Hall Effect v B ???? - + When does it reach equilibrium? E h V>0

  26. Hall Effect for Opposite Charges E E v v B B >0 ???? V>0 - - + + V<0

  27. Hall Effect Edwin Herbert Hall (1855 - 1938) By measuring the Hall effect for a particular material, we can determine the sign of the moving particles that make up the current

  28. Hall Effect in a Metal What is the magnitude of the Hall effect in a metal? V Measure know the charge (e) Then we can find n Monovalent metals:n is the same as # of atoms per m3 Some metals:n is larger than # of atoms per m3

  29. Clicker Question • Voltmeter 1 reading is POSITIVE • Voltmeter 2 reading is POSITIVE • Mobile charges are: • A) Positive (holes) • B) Negative (electrons) • C) Not enough information

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