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Electric Currents and Magnetic Fields

This video explains how electric currents produce magnetic fields and the force exerted on current-carrying wires in a magnetic field. It also introduces the concept of magnetic force on charged particles and the right-hand rule.

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Electric Currents and Magnetic Fields

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  1. Chapter 27Magnetism

  2. 27-2 Electric Currents Produce Magnetic Fields https://www.youtube.com/watch?v=tKxFLH2Nhe4

  3. 27-2 Electric Currents Produce Magnetic Fields Experiment shows that an electric current produces a magnetic field. The direction of the field is given by a right-hand rule.

  4. 27-2 Electric Currents Produce Magnetic Fields Here we see the magnetic field due to a current loop; the direction is again given by a right-hand rule.

  5. 27-2 Electric Currents Produce Magnetic Fields https://www.youtube.com/watch?v=F1PWnu01IQg

  6. A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.

  7. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation: In vector notation:

  8. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Unit of B: the tesla, T: 1 T = 1 N/A·m. Another unit sometimes used: the gauss (G): 1 G = 10-4 T. Directions of the Magnetic Field:

  9. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-1: Magnetic Force on a current-carrying wire. A wire carrying a 30-A current has a length l =12 cm between the pole faces of a magnet at an angle θ = 60, as shown. The magnetic field is approximately uniform at 0.90 T. We ignore the field beyond the pole pieces. What is the magnitude and direction of the force on the wire?

  10. Problem 8 • (II) A long wire stretches along the x axis and carries a 3.0-A current to the right (+x). The wire is in a uniform magnetic field • Determine the components of the force on the wire per cm of length.

  11. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-2: Measuring a magnetic field. A rectangular loop of wire hangs vertically as shown. A magnetic field B is directed horizontally, perpendicular to the wire, and points out of the page at all points. The magnetic field is very nearly uniform along the horizontal portion of wire ab (length l = 10.0 cm) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward magnetic force (in addition to the gravitational force) of F = 3.48 x 10-2 N when the wire carries a current I = 0.245 A. What is the magnitude of the magnetic field B?

  12. 27-4 Force on an Electric Charge Moving in a Magnetic Field The force on a moving charge is related to the force on a current: Once again, the direction is given by a right-hand rule.

  13. Magnetic Forceon a point charge Force on a moving charge = out of page Arrow coming at you = into page Arrow leaving you Direction: Right hand rule is Perpendicular to both and Lay hand along palm toward q  Thumb points along q  Thumb points opposite

  14. Magnetic Force on a point charge Direction: RIGHT Hand Rule F Perpendicular to both v and B Here Into or Out of the page Run fingers along v, curl them towards B, • • If q is positive, thumb points along F • If q is negative, thumb point opposite F

  15. Problem 17 • 17.(I) Determine the direction of for each case in Fig. 27–43, where represents the maximum magnetic force on a positively charged particle moving with velocity

  16. 27-4 Force on an Electric Charge Moving in a Magnetic Field If a charged particle is moving (electron) perpendicular to a uniform magnetic field, its path will be a circle, and the magnetic force is towards the center. What will be the direction of the force if you have a proton?

  17. 27-4 Force on an Electric Charge Moving in a Magnetic Field Example 27-7: Electron’s path in a uniform magnetic field. An electron travels at 2.0 x 107 m/s in a plane perpendicular to a uniform 0.010-T magnetic field. Describe its path quantitatively.

  18. 27-4 Force on an Electric Charge Moving in a Magnetic Field Problem solving: Magnetic fields – things to remember: • The magnetic force is perpendicular to the plane formed by magnetic field and velocity. • The right-hand rule is useful for determining directions. The right-hand rule gives the direction. • Equations in this chapter give magnitudes only.

  19. 27-4 Force on an Electric Charge Moving in a Magnetic Field

  20. Charged particles in B-fields • Aurora Borealis: Northern Lights • Aurora Australis: Southern Lights • Due to ions (e- & p+) from the Sun • Travel from Sun to Earth in ~ 3 days • 93 million miles in 3 days ~ 30 million miles/day www.spaceweather.com Aurora on 11/20/03, Zagreb, Croatia. Photo by HrvojeHorvat http://www.nasa.gov/mpg/143772main_SolarCycleCME_Reconnection.mpg

  21. Aurora Ions steered to poles by Earth’s mag. field • Collide with molecules in atmosphere • ionize particles, recombination produces light: Aurora • More energetic particles get closer to Earth http://www.swpc.noaa.gov/pmap/

  22. Lorentz Equation

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