1 / 48

Magnetic Force on a Current Element

Magnetic Force on a Current Element. Magnetic Force on a Current Element Magnetic Force on Current in a Straight Wire Magnetic Force on a Current Loop Applications: Hall Effect, Motor, Cyclotron. Reading Question.

presley
Download Presentation

Magnetic Force on a Current Element

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magnetic Force on a Current Element Magnetic Force on a Current Element Magnetic Force on Current in a Straight Wire Magnetic Force on a Current Loop Applications: Hall Effect, Motor, Cyclotron

  2. Reading Question What is the current direction in this loop? And which side of the loop is the north pole? 1. Current clockwise; north pole on top 2. Current counterclockwise, north pole on top 3. Current clockwise; north pole on bottom 4. Current counterclockwise, north pole on bottom

  3. Reading Question What is the current direction in this loop? And which side of the loop is the north pole? 1. Current clockwise; north pole on top 2. Current counterclockwise, north pole on top 3. Current clockwise; north pole on bottom 4. Current counterclockwise, north pole on bottom

  4. Reading Question What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? 1. Helix 2. Parabola 3. Circle 4. Ellipse 5. Hyperbola

  5. Reading Question What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? 1. Helix 2. Parabola 3. Circle 4. Ellipse 5. Hyperbola

  6. Reading Question An electron moves perpendicular to a magnetic field. What is the direction of ? 1. Left 2. Up 3. Down 4. Into the page 5. Out of the page

  7. Reading Question An electron moves perpendicular to a magnetic field. What is the direction of ? 1. Left 2. Up 3. Down 4. Into the page 5. Out of the page

  8. Magnetic Force on a Moving Charge • Magnetic Force on a Moving Charge Write the equation that expresses the magnetic force on a current element in a magnetic field.

  9. positive charge negative charge negative charge positive charge negative charge positive charge Student Notebook

  10. Student Notebook

  11. Student Notebook

  12. Magnetic Force on a Current Element • Magnetic Force on a Current Element Write the equation that expresses the magnetic force on a current element in a magnetic field. What is dl in this equation? Discuss this and write your answer. From the expression for dF find the magnetic force on a long straight wire carring a current. An infinitesimal length in the direction of the current.

  13. Magnetic Force on a Current Element • Magnetic Force on a Current Element Let’s derive this relationship from the magnetic force on a moving charge. What is the equation? But there are nAl charges in a current with cross-sectional area A and length l. • A wire is stretched from the front of the room to the back with the current flowing toward the front. If the earths magnetic field points straight down, what is the direction of the force on the wire? Discuss this in your group.

  14. Student Notebook

  15. Student Notebook

  16. Student Notebook

  17. Magnetic Force on a Current Element

  18. Magnetic Force on a Current Element • Application A coat hanger is bent in a U shape as shown below. If the coat hanger carries a current of 3 A and is in a constant magnetic field of 0.2 T pointing straight down (into the page), what is the total force on the coat hanger? Discuss how to attack this problem in your group before you start to work the problem.

  19. Magnetic Force on a Current Element • Application I = 3 A B = 0.2 T into page

  20. Magnetic Force on a Current Element • Magnetic Force Between Two Currents What is the force on a current element in a magnetic field? What is the angle between Idl and B? What is the magnetic field for a wire? 90 degrees

  21. Magnetic Force on a Current Element • What happen? • Just an example of

  22. Magnetic Force on a Current Element • Motion of a Charge Particle in a Magnetic Field

  23. Magnetic Force on a Current Element • Mass Spectrometer

  24. Magnetic Force on a Moving Charge • Particle Accelerator: Cyclotron

  25. Magnetic Force on a Moving Charge • Aurora

  26. Magnetic Force on a Current Element • Why is there a magnetic force on a current?

  27. Magnetic Force on a Current Element • What is the Hall Effect? In a semiconductor you have both positive and negative charge carriers. The negative charge carriers are electrons and the positive charge carriers are called “holes”. They behave like positive electrons.

  28. Magnetic Force on a Current Element • How do speakers work?

  29. Magnetic Force on a Current Element • A Current Loop in a Magnetic Field On the table you will find a square wire loop with a wood rod through the center of the loop as shown below. Cut a small arrow and tape it to the loop. This is to show the direction of the current in the loop. One member of the group should hold the loop between their hands by the rod so that the rod is parallel to the long side of the table and the current is flowing to the right along the top side. Assume the magnetic field is points toward the center of the table and perpendicular to the edge of the table. Use a pencil to represent the magnetic field.

  30. Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Find the force (magnitude and direction) on the two sides of the loop (Fright, Fleft) where the rod is connected. Can you show that these two force always cancel out no matter what the orientation of the loop?

  31. q q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Next find the force (magnitude and direction) on the top of the loop. Finally find the force on the bottom of the loop.

  32. q q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Have someone pull on the top and bottom in the direction of the forces and describe what happens to the loop. What is the total force in terms of the current, length of the loop side, and the magnetic field?

  33. q q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Oh, so long ago we studied the torque. The torque was defined as and the magnitude was given by What is r? r is a vector pointing from the axis of rotation to where the force is applied.

  34. q q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Use the last figure and equation for the force to find the magnitude of the torque on the loop.

  35. Magnetic Force on a Current Element • A Current Loop in a Magnetic Field

  36. q is our old vector area q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field Can you show that this is the same as Equation (29-9)? What is ? Finally, we define the magnetic dipole moment similar to the electric dipole moment where Show that the torque is

  37. q q q Magnetic Force on a Current Element • A Current Loop in a Magnetic Field What is the equation for the energy of a magnetic dipole in a magnetic field? What position is the loop when the energy is the lowest? Is the magnetic dipole moment parallel or anti-parallel to the magnetic field? Explain. When m and B are in opposite directions

  38. Magnetic Force on a Current Element • Demonstration: Motor

  39. Magnetic Force on a Current Element • Demonstration: Motor The instructor (that's me) will show you a St. Louis motor. With the bar magnetic removed and the battery connected to the motor coil with a key switch, press the key switch and use a compass to determine the north and south poles of the armature (coil). Label the poles on the diagram.

  40. Magnetic Force on a Current Element Demonstration: Motor • Next we will rotate the coil by 180 degrees and determine the poles of the armature again? Did they stay the same? Explain what happens as the coil rotates. • When a north magnetic pole is placed on the left will the armature be attracted or repelled? • What about a south pole on the right side? • When the coil rotates 180 degrees will the armature be repelled or attracted? Is this the same as before?

  41. Magnetic Force on a Current Element Demonstration: Motor • Let’s try it. Hold the coil so that it is parallel (as below) to the magnetic and press the key switch. Does this agree with your thinking above? • This can also be explained by a magnetic dipole in a magnetic field. Return the armature to the original position. From the direction of the current determine the direction of the dipole moment, m. Draw an arrow in the direction of the magnetic dipole moment and label m. From the two bar magnetic determine the direction of the magnetic field. Use the equation for the torque on a magnetic dipole to explain if the coil is attracted or repelled in this position. Does it agree with what you did above?

  42. Magnetic Force on a Current Element • Demonstration: Motor • Use energy considerations to determine which way the coil will rotate. Let the coil go and observe the rotation of the coil. Does it agree. m N S

  43. Student Notebook

  44. Student Notebook

  45. Magnetic Force on a Current Element • Application: MRI or NMR

  46. Magnetic Force on a Current Element • Magnetic Materials table Paramagnetic Diamagnetic Ferromagnetic

  47. Magnetic Force on a Current Element • What if the wire is not straight? In general this is a diffuliculte problem to solve, but there are a few cases that are easy to solve. One is a semi-circular arc shown here.

  48. The force is out of the page Magnetic Force on a Current Element • What if the wire is not straight? What do we ask?

More Related