PHYS 202. Lecture 7 Professor Stephen Thornton February 9, 2006

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1 PHYS 202 Lecture 7 Professor Stephen Thornton February 9, 2006

2 Reading Quiz What is the result when we break a thin bar magnet in two pieces? 1. One piece has only a N pole. The other piece only a S pole. 2. One piece is still a bar magnet. The other piece is not a bar magnet. 3. Both pieces are bar magnets. 4. It depends on the magnet material.

3 Answer: 3 Try it and see. Both pieces become bar magnets. We have never seen a single magnetic pole.

4 Last Time More conceptual quizzes Kirchhoff s rules Capacitors in series and parallel RC circuit had to hurry

5 Today Review RC circuits Discuss meters Discuss applications Magnetism: iron filings, poles, bar magnets Magnetic field and magnetic force Motion of charged particle in magnetic field Exam I, Thursday, Feb. 16, Chs , 20 multiple choice questions.

6 Review RC time constant demo t / τ qt () = Qe = CV Q V = e = V e C V t/ τ t/ τ 0 C is charged. Bullet cuts Gate 1; C discharges through resistor. Bullet cuts Gate 2; C stops discharging. Electrometer measures voltage drop across C.

7 V = V e V / V = t / τ 0 e t / τ ln( V / V ) = t/ τ ln( V / V) = t/ τ t = τ ln( V / V) = RCln( V / V) ( )( F)ln( 0 / ) t = Ω V V 3 ( 3 ) 2.2 t = s ln( V0 / V) = s ln t = s d 1.0 m v = = = 127 m/s 3 Speed calculation

8 Applications of capacitors are numerous Intermittent windshield wipers Flashing yellow lights for safety Turn signals on car Flashing Christmas tree lights Camera photoflash Defibrillator need energy delivered quickly Computer keyboard keys act as capacitor Stud finder - demonstrate

9 Work Problems

10 Measuring the Current in a Circuit Ammeter We want ammeter to have very low resistance so it will not affect circuit. Ammeters go in series.

11 Measuring the Voltage in a Circuit Voltmeter = + R R R eq voltmeter We want voltmeter to have very large resistance so it will not affect circuit. Voltmeters go in parallel across what is being measured.

12 Show digital multimeter and use it to measure resistance, capacitance, and voltage.

13 Conceptual Quiz A resistor and an initially uncharged capacitor arranged in series are charged by a battery, which is connected at t = 0. Just after t = 0 the current in the circuit t = 0 1. is constant because the emf supplied by the battery is constant. 2. decreases exponentially in time. 3. increases exponentially in time. 4. There is no current because the electrons cannot flow through the gap in the capacitor.

14 The current flows initially because the capacitor acts like a short circuit until charge builds up on its two opposite plates. Then the current decreases exponentially. Answer: 2

15 Ch Magnetism Do demos with iron filings and magnets. Learn about magnetic fields. Do demo with tiny magnetic arrows on overhead projector. Demonstrates directions of magnetic fields.

16 Some interesting facts Magnets come with N and S poles. Have never found an isolated pole. (monopole) Lodestone has been known for centuries; used in navigation for almost 1000 years. The direction of the magnetic field is the direction that the N pole of a magnet points. Magnetic fields make loops never start and stop. (no magnetic monopoles, do have dipoles) Magnetic field lines exit from the N pole and enter the S pole of a bar magnet. SI unit is tesla - T

17 Magnets Always Have Two Poles

18 Magnetic Field Lines for a Bar Magnet S N B Imagine using a test pole N; place it at any point and see where the force is. Just like we do for electric fields. We actually use small compasses to do this.

19 Do demo on magnetic deflection of an electron beam. The result is that there is a force on a moving charge in a magnetic field.

20 Magnetic Force on a Moving Charge Look at e -

21 The Magnetic Force on a Moving Charged Particle We find maximum force when v B

22 The Magnetic Force Right-Hand Rule F = qv B B ***

23 Magnetic Field of the Earth

24 Van Allen Belts (1958)

25 Aurora borealis (northern lights)

26 Helical Motion in a Magnetic Field Remember F = qv B

27 Convention to show vector directions Point of arrow Feather of arrow

28 The Magnetic Force for Positive and Negative Charges F = qv B B

29 Conceptual Quiz A beam of electrons enters a region with a magnetic field as shown below. If the beam is deflected upward, the magnetic field must be oriented 1. downward 2. up 3. into the plane of the drawing 4. out of the plane of the drawing 5. to the left 6. to the right 7. none of the above - it is at an angle 8. need more information to determine

30 Conceptual Quiz A beam of electrons enters a region with a magnetic field as shown below. If the beam is deflected upward, the magnetic field must be oriented F = qv B B 1. downward 2. up 3. into the plane of the drawing 4. out of the plane of the drawing 5. to the left 6. to the right 7. none of the above - it is at an angle 8. need more information to determine

31 Answer: 3 A beam of electrons enters a region with a magnetic field as shown below. If the beam is deflected upward, the magnetic field must be oriented F = qv B B Force is up, so place right thumb up. Velocity is to left, so point fingers to the left. Curl your fingers towards you. Direction is towards us. But charge is negative, so we reverse directions, and find that direction of magnetic field is into plane. Answer is 3.

32 Circular Motion in a Magnetic Field

33 Charged Particle in a Circular Path

34 Operating Principle of a Mass Spectrometer r = mv qb *** Several applications

35 Forces on a charged particle that is moving perpendicularly to a uniform magnetic field. Principle of cyclotron

36 Magnetic Force on a Current-Carrying Wire F = qv B L F = q B t q F = L B t F = IL B *** F = ILBsinθ

37 Conceptual Quiz A negative particle moves upward along the trajectory shown. A magnetic field points toward the right. In which direction is the magnetic force on the particle? 1. up 2. down 3. into the plane of the drawing 4. out of the plane of the drawing 5. left 6. right

38 Answer: 4 Use the right hand rule to determine that the force must be out of the plane.

Conceptual Quiz Cosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth's surface if most of them were not deflected by Earth's magnetic field.

39 Conceptual Quiz Cosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth's surface if most of them were not deflected by Earth's magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the 1. poles. 2. mid-latitudes. 3. equator.

40 Answer: 1 We showed earlier that particles come in near the Earth and are affected by the Earth s magnetic field. They feel a force and are deflected into spirals and spiral towards the N and S poles.

41 Conceptual Quiz A beam of atoms enters a magnetic field region. What path will the atoms follow? 1 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 x x x x x x x x x x x x x x x x x x 4 x x x x x x x x x x x x 2 3

42 Conceptual Quiz A beam of atoms enters a magnetic field region. What path will the atoms follow? 1 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 x x x x x x x x x x x x x x x x x x 4 x x x x x x x x x x x x 2 3 Atoms are neutral objects whose net charge is zero. Thus they do not experience a magnetic force. Follow-up: What charge would follow path #3? What about path #1?

Charging a Capacitor in RC Circuits

Lecture 8-18 Charging a Capacitor in RC Circuits 1. Charging equation: From Kirchhoff's Law q ε t/ RC t/ τ ε ir = 0 i = e = I0e C R 2. Switch closed at t = 0. Initially C is uncharged. ΔV C across C is