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Understanding Magnetic Fields in Physics

Delve into the fundamentals of magnetism, magnetic fields, and their applications in physics. Learn how to calculate and utilize magnetic fields effectively in various scenarios. Explore topics such as magnetic dipoles, Ampère’s Law, magnetic forces, and more.

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Understanding Magnetic Fields in Physics

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  1. Chapter 33. The Magnetic Field Digital information is stored on a hard disk as microscopic patches of magnetism. Just what is magnetism? How are magnetic fields created? What are their properties? These are the questions we will address. Chapter Goal: To learn how to calculate and use the magnetic field.

  2. Chapter 33. The Magnetic Field Topics: • Magnetism • The Discovery of the Magnetic Field • The Source of the Magnetic Field: Moving Charges • The Magnetic Field of a Current • Magnetic Dipoles • Ampère’s Law and Solenoids • The Magnetic Force on a Moving Charge • Magnetic Forces on Current-Carrying Wires • Forces and Torques on Current Loops • Magnetic Properties of Matter

  3. Chapter 33. Reading Quizzes

  4. What is the SI unit for the strength of the magnetic field? • Gauss • Henry • Tesla • Becquerel • Bohr magneton

  5. What is the SI unit for the strength of the magnetic field? • Gauss • Henry • Tesla • Becquerel • Bohr magneton

  6. What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? • Helix • Parabola • Circle • Ellipse • Hyperbola

  7. What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? • Helix • Parabola • Circle • Ellipse • Hyperbola

  8. The magnetic field of a point charge is given by • Biot-Savart’s law. • Faraday’s law. • Gauss’s law. • Ampère’s law. • Einstein’s law.

  9. The magnetic field of a point charge is given by • Biot-Savart’s law. • Faraday’s law. • Gauss’s law. • Ampère’s law. • Einstein’s law.

  10. The magnetic field of a straight, current-carrying wire is • parallel to the wire. • inside the wire. • perpendicular to the wire. • around the wire. • zero.

  11. The magnetic field of a straight, current-carrying wire is • parallel to the wire. • inside the wire. • perpendicular to the wire. • around the wire. • zero.

  12. Chapter 33. Basic Content and Examples

  13. Tactics: Right-hand rule for fields

  14. The Source of the Magnetic Field: Moving Charges The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law: where r is the distance from the charge and θ is the angle between v and r. The Biot-Savart law can be written in terms of the cross product as

  15. EXAMPLE 33.1 The magnetic field of a proton QUESTION:

  16. EXAMPLE 33.1 The magnetic field of a proton

  17. EXAMPLE 33.1 The magnetic field of a proton

  18. EXAMPLE 33.1 The magnetic field of a proton

  19. EXAMPLE 33.1 The magnetic field of a proton

  20. EXAMPLE 33.1 The magnetic field of a proton

  21. The Magnetic Field of a Current The magnetic field of a long, straight wire carrying current I, at a distance d from the wire is The magnetic field at the center of a coil of N turns and radius R, carrying a current I is

  22. Problem-Solving Strategy: The magnetic field of a current

  23. Problem-Solving Strategy: The magnetic field of a current

  24. Problem-Solving Strategy: The magnetic field of a current

  25. Problem-Solving Strategy: The magnetic field of a current

  26. EXAMPLE 33.4 The magnetic field strength near a heater wire QUESTION:

  27. EXAMPLE 33.4 The magnetic field strength near a heater wire

  28. EXAMPLE 33.4 The magnetic field strength near a heater wire

  29. EXAMPLE 33.4 The magnetic field strength near a heater wire

  30. Tactics: Finding the magnetic field direction of a current loop

  31. Magnetic Dipoles The magnetic dipole moment of a current loop enclosing an area A is defined as The SI units of the magnetic dipole moment are A m2. The on-axis field of a magnetic dipole is

  32. EXAMPLE 33.7 The field of a magnetic dipole QUESTIONS:

  33. EXAMPLE 33.7 The field of a magnetic dipole

  34. EXAMPLE 33.7 The field of a magnetic dipole

  35. EXAMPLE 33.7 The field of a magnetic dipole

  36. Tactics: Evaluating line integrals

  37. Ampère’s law Whenever total current Ithrough passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère’s law:

  38. The strength of the uniform magnetic field inside a solenoid is where n = N/l is the number of turns per unit length.

  39. The Magnetic Force on a Moving Charge The magnetic force on a charge q as it moves through a magnetic field B with velocity v is where α is the angle between v and B.

  40. Magnetic Forces on Current-Carrying Wires Consider a segment of wire of length l carrying current I in the direction of the vector l. The wire exists in a constant magnetic field B. The magnetic force on the wire is where α is the angle between the direction of the current and the magnetic field.

  41. EXAMPLE 33.13 Magnetic Levitation QUESTION:

  42. EXAMPLE 33.13 Magnetic Levitation

  43. EXAMPLE 33.13 Magnetic Levitation

  44. EXAMPLE 33.13 Magnetic Levitation

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