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Lesson 7

Lesson 7. Magnetic Fields. Magnetic Force on moving charge Motion of charge in Magnetic Field Magnetic Force on current carrying conductor Torque on current carrying loop Hall Effect Magnetic Devices. Magnetic Force. Some metallic objects cause other metallic objects to accelerate

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Lesson 7

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  1. Lesson 7 Magnetic Fields • Magnetic Force on moving charge • Motion of charge in Magnetic Field • Magnetic Force on current carrying conductor • Torque on current carrying loop • Hall Effect • Magnetic Devices

  2. Magnetic Force • Some metallic objects cause other metallic objects to accelerate • Thus must be producing a force • This force is different to Gravitational Force and Electric Force • Can plot the directions of lines force • Lines of motion of effected objects • MAGNETIC FORCE

  3. Magnetic Field Lines

  4. Properties of Magnetic Fields • Properties • Moving charge (current) is effected • Force proportional • Q and v • FB = 0 if v parallel to Magnetic Field B • FBperpendicular to v and B • FB on positive charge opposite to that on negative charge • FB proportional to Sin of the angle v makes with B

  5. Mathematical Expression

  6. Vector Product I Vector Product = + + A i j k A A A x y z = + + B i j k B B B x y z i j k A A A A A A y z x y x z ´ = = - + A B i j k A A A x y z B B B B B B y z x y x z B B B x y z ( ) ( ) ( ) = - - - + - i j k A B A B A B A B A B A B y z z y x z z x x y y x

  7. Vector Product II

  8. Unit vector products

  9. Work done by Magnetic Field Work Done by Magnetic Force on charge

  10. Work done by Electric Field Compare to Electric Force

  11. Implications • Thus Kinetic Energy of charge is not changed by FB • Potential Energy is not changed

  12. SI units

  13. Magnetic Flux

  14. Right Hand Rule

  15. Magnetic Force on Moving Charge B v Q k j FB i = ´ = - ´ F v B Q j k Q v B B y z i j k = - ´ = - = - j k i Qv B Qv B 0 1 0 Qv B y z y z y z 0 0 1

  16. Mathematical expression

  17. Uniform Circular Motion of Charge Uniform Circular Motion i j k

  18. Mathematical analysis 2 F v QvB = = = a c r m m 2 mv Þ = QvB r mv = r radius of motion QB w v = r BQ rad \ w = angular speed = angular freqency ( ) s m w BQ = = f frequency ( cps = Hz ) p p 2 2 m p 1 2 m = = T period of the motion . f BQ

  19. Magnetic Bottles magnetic bottles

  20. Vector Integral I ds b rb B vector integral ra a I

  21. Vector Integral II ds b rb B rb- ra ra a I

  22. Vector Integral III Sum ds

  23. Magnetic Force on Current Force on current carrying conductor in a uniform magnetic field : ò b = ´ = ´ F s B l B I d I B a ( ) = - l r r where a b é ù æ ö ds dQ ( ) = = = = ç ÷ v s s s s ê dQ dQ ˆ ds ˆ Ids ˆ Id ú è ø ë û dt dt

  24. Magnetic Force on Current Loop I Force on Current Loop I B k j i

  25. Magnetic Force on Current Loop II Total Force on Loop

  26. Torque on Current Loop I Torque on Current Loop  I B  k z  j  i  y

  27. Torque on Current Loop II

  28. Torque on Current Loop III

  29. Magnetic Moment

  30. Oriented Area Vector A=Ai: Area vector with orientation I k A j i

  31. Hall Effect I Hall Effect A d t vd FE FB B - + V E

  32. Mathematical analysis At Equlibrium = F F E B V = E d = = = F F eE v eB E B d E \ = v d B J I = = Remember v d ne neA I E BI BI BI \ = Þ = = = n V neA B EAe Vte dte d

  33. Measurement can measure vdby measuring the PD V.

  34. Lorentz Force

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