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Magnetism

Magnetism. N. S. Magnetic Dipole. Magnetic Field (B). Magnetic Monopoles. Do not exist! They differ from electric dipoles, which can be separated into electric monopoles. Magnetic Force on Charged Particle. magnitude: F = qvBsinθ q: charge in Coulombs v: speed in meters/second

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Magnetism

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  1. Magnetism

  2. N S MagneticDipole Magnetic Field (B)

  3. Magnetic Monopoles • Do not exist! • They differ from electric dipoles, which can be separated into electric monopoles.

  4. Magnetic Force on Charged Particle magnitude: F = qvBsinθ q: charge in Coulombs v: speed in meters/second B: magnetic field in Tesla θ: angle between v and B direction: Right Hand Rule

  5. Magnetic Force Calculate the magnitude and direction of the magnetic force. v = 300,000 m/s 34o q = 3.0mC B = 200 mT

  6. Magnetic Fields • Formed by moving charge • Affect moving charge

  7. Magnetic Field Visualization

  8. 3D Magnetic Field Visualization

  9. 3D Magnetic Field Visualization

  10. 3D Magnetic Field Visualization

  11. Magnetic Forces can... • accelerate charged particles by changing their direction • cause charged particles to move in circular or helical paths

  12. Magnetic Forces cannot... • change the speed or kinetic energy of charged particles • do work on charged particles

  13. B V F V F F F V V When v and B are at right angles to each other... qvBsinθ = mv2/r qB = mv/r q/m = v/(rB) x into • out q is +

  14. When v and B are at right angles to each other...

  15. F F v X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Up Up v F + Left + - · · · · · · · · · · · · · · · · v F · · · · · · · · Right - · · · · · · · · v Practice With Directions: What is the direction of the force F on the charge in each of the examples described below? negative q

  16. Circular Paths in Magnetic Field Fmagnetic = Fcentripetal qvB = mv2/r

  17. Electron Beam in Magnetic Field

  18. B q E Electric and Magnetic Fields Together v = E/B

  19. Magnetic Force on Current-carrying Wire • F = I L B sinθ • I: current in Amps • L: length in meters • B: magnetic field in Tesla • θ: angle between current and field

  20. MAGNETIC FIELD PRODUCED BY CURRENT CARRYING WIRE A long, straight current carrying wire produces a magnetic field.

  21. Magnetic Field forLong Straight Wire • B = μoI/(2πr) • μo: 4π x 10-7Tm/A • magnetic permeability of free space • I: current (A) • r: radial distance from center of wire (m)

  22. r x • Hand Rule i • Curve your fingers • Place your thumb in direction of current. • Curved fingers represent curve of magnetic field. • Field vector at any point is tangent to field line.

  23. I For straight currents

  24. Principle of Superposition When there are two or more currents forming a magnetic field, calculate B due to each current separately and then add them together using vector addition.

  25. Wires attract if currents in same direction Wires repel if currents in opposite direction   Force Between Current Carrying Wires

  26. Magnetic Field Inside aSolenoid • B = μonI • μo: 4π x 10-7Tm/A • n: number of coils per unit length • I: current (A)

  27. N I S Lab: Magnetic Field Map • Using a compass, map the magnetic field inside and outside your solenoid. Show: • Current through solenoid • Connection to DC outlet • Field lines mapped with compass • Edge effects (What happens to those field lines farther away from the solenoid?) • North and South Poles of solenoid

  28. Lab EvaluationMagnetic Field MapA) Are field lines visible in the core of the solenoid?B) Are the directions of the field lines in the core consistent with the Right Hand Rule?C) Are the North and South Poles correctly identified?

  29. Magnetic Flux • The product of magnetic field and area. • Can be thought of as a total magnetic “effect” on a coil of wire of a given area.

  30. Φ = BA Φ  = BA cos θ Magnetic flux

  31. Magnetic Flux B = BAcosθ B: magnetic flux in Webers (Tesla meters2) B: magnetic field in Tesla A: area in meters2. θ: the angle between the area and the magnetic field.

  32. Magnetic Flux • A system will respond so as to oppose changes in magnetic flux. • Changing the magnetic flux can generate electrical current.

  33. A Change in Flux By changing the field strength B going through a constant loop area A: ΔΦ = ΔB A

  34. A Change in Flux By changing the effective area A in a constant magnetic field B:ΔΦ = B ΔA

  35. Faraday’s Law of Induction E = -NB/Δt E: induced potential (V) N: # loops B: magnetic flux (Webers, Wb) t: time (s)

  36. A closer look … E = -ΔB/Δt E = -Δ(BAcosθ)/Δt • To generate voltage • Change B • Change A • Change θ

  37. Lenz’s Law • The current will flow in a direction so as to oppose the change in flux. • Use in combination with hand rule to predict current direction.

  38. (a)As the magnet moves to the right, B increases. (b) To oppose increased B , the inducedB must be opposite to that of the bar magnet. The inducedI must be CCW

  39. When N of magnet is pushed into a loop the B↑. Upward B is induced. As viewed from above, the induced current must flow CCW

  40. When N of magnet is pulled away from loop the B↑. Downward B is induced. As viewed from above, the induced current must flow CW

  41. Motional emf E = B L v E : induced potential L: length of bar or wire V: speed of bar or wire

  42. Wire is pulled to the right by an unseen force. Induced emf = BLv Induced EMF

  43. ΔB = Δ(BA)  ΔB = B ΔA     ΔB = B(L Δx) Δ B /Δt  = BLx/t Δ B /Δt  = BLv Induced EMF

  44. 2002B5 p.49 A proton of mass mp and charge e is in a box that contains an electric field E, and the box is located in Earth's magnetic field B.The proton moves with an initial velocity vertically upward from the surface of Earth. Assume gravity is negligible.

  45. 2002B5 p.49 (a)On the diagram, indicate the direction of the electric field inside the box so that there is no change in the trajectory of the proton while it moves upward in the box. Explain yourreasoning.

  46. 2002B5 p.49 (b)Determine the speed v of the proton while in the box if it continues to move vertically upward. Express your answer in terms of the fields and the given quantities.

  47. 2002B5 p.49 The proton now exits the box through the opening at the top. (c) On the figure, sketch the path of the proton after it leaves the box.

  48. 2002B5 p.49

  49. 2002B5 p.49 (d) Determine the magnitude of the acceleration a of the proton just after it leaves the box, in terms of the given quantities and fundamental constants.

  50. 1978B4 p.51 Two parallel conducting rails, separated by a distance L of 2 m, are connected through a resistance R of 3 Ω as shown. A uniform magnetic field with a magnitude B of 2 T points into the page. A conducting bar with mass m of 4 kg can slide without friction across the rails.

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