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Physics 212 Lecture 12

Physics 212 Lecture 12. Today's Concept: Magnetic Force on moving charges. Main Point 1. First, we introduced some observations involving forces exerted by bar magnets and between current carrying wires to indicate the existence of a new kind of phenomena in the world that we call magnetism.

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Physics 212 Lecture 12

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  1. Physics 212 Lecture 12 Today's Concept: Magnetic Force on moving charges

  2. Main Point 1 First, we introduced some observations involving forces exerted by bar magnets and between current carrying wires to indicate the existence of a new kind of phenomena in the world that we call magnetism

  3. Main Point 2 Second, we made the claim that all magnetic effects can be described in terms of a magnetic field that is created by the motion of electric charges, i.e., electric currents.

  4. Main Point 3 Third, these magnetic fields exert forces on electric charges that are in motion. We introduced the mathematical form for this force in terms of a cross product of vectors. In particular, the magnetic force on charge q moving with velocity v through a region containing a magnetic field B is given by qvcrossB.

  5. Magnetic Observations Magnetic Charge? cut in half N S N S N S • Bar Magnets • Compass Needles N S N S S N N S N S 07

  6. Magnetic Observations V V V V I F I F F I I F • Compass needle deflected by electric current I • Magnetic fields created by electric currents • Magnetic fields exert forces on electric currents (charges in motion) 12

  7. Magnetism & Moving Charges Next Week All observations are explained by two equations: Today 14

  8. Cross Product Review • Cross Product different from Dot Product • A●Bis a scalar; A x B is a vector • A●Bproportional to the component of B parallel to A • A x B proportional to the component of B perpendicular to A • Definition of A x B • Magnitude: ABsinq • Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule 16

  9. Checkpoint 1a Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: A B C D E 18

  10. Checkpoint 1b Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: A B C D E 21

  11. Cross Product Practice • protons (positive charge) coming out of screen • Magnetic field pointing down • What is direction of force on POSITIVE charge? A) Left B) Right C) UP D) Down E) Zero + y - y - x + x y x B screen z 24

  12. Motion of Charge q in Uniform B Field q q q q 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 x x x x x x x x x x F F v v F F v • Force is perpendicular to v • Speed does not change • Uniform Circular Motion • Solve for R: R UniformBinto page Demo 30

  13. . B Checkpoint 2a The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. A B C D 34

  14. Checkpoint 2b The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. A B C 36

  15. Calculation • Conceptual Analysis • What do we need to know to solve this problem? (A) Lorentz Force Law (B) E field definition (C) V definition (D) Conservation of Energy/Newton’s Laws (E) All of the above exits here A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. What is B? x0/2 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 X X X X E q,m x0 d enters here B B

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