Chap 26 SM - Chapter 26 The Magnetic Field Conceptual...

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499 Chapter 26 The Magnetic Field Conceptual Problems 1 [SSM] When the axis of a cathode-ray tube is horizontal in a region in which there is a magnetic field that is directed vertically upward, the electrons emitted from the cathode follow one of the dashed paths to the face of the tube in Figure 26-30. The correct path is ( a ) 1, ( b ) 2, ( c ) 3, ( d ) 4, ( e ) 5. Determine the Concept Because the electrons are initially moving at 90 ° to the magnetic field, they will be deflected in the direction of the magnetic force acting on them. Use the right-hand rule based on the expression for the magnetic force acting on a moving charge B v F r r r × = q , remembering that, for a negative charge, the force is in the direction opposite that indicated by the right-hand rule, to convince yourself that the particle will follow the path whose terminal point on the screen is 2. ) ( b is correct. 2 •• We define the direction of the electric field to be the same as the direction of the force on a positive test charge. Why then do we not define the direction of the magnetic field to be the same as the direction of the magnetic force on a moving positive test charge? Determine the Concept The direction of the force depends on the direction of the velocity. We do not define the direction of the magnetic field to be in the direction of the force because if we did, the magnetic field would be in a different direction each time the velocity was in a different direction. If this were the case, the magnetic field would not be a useful construct. 3 [SSM] A flicker bulb is a light bulb that has a long, thin flexible filament. It is meant to be plugged into an ac outlet that delivers current at a frequency of 60 Hz. There is a small permanent magnet inside the bulb. When the bulb is plugged in the filament oscillates back and forth. At what frequency does it oscillate? Explain. Determine the Concept Because the alternating current running through the filament is changing direction every 1/60 s, the filament experiences a force that changes direction at the frequency of the current. 4 In a cyclotron, the potential difference between the dees oscillates with a period given by T = 2 π mq B () . Show that the expression to the right of the equal sign has units of seconds if q , B and m have units of coulombs, teslas and kilograms, respectively.
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Chapter 26 500 Determine the Concept Substituting the SI units for q , B , and m yields: s 1 m kg s m kg kg m s s m kg kg m C s N C kg m A N C kg T C 2 = = = = = 5 A 7 Li nucleus has a charge equal to +3 e and a mass that is equal to the mass of seven protons. A 7 Li nucleus and a proton are both moving perpendicular to a uniform magnetic field B r . The magnitude of the momentum of the proton is equal to the magnitude of the momentum of the nucleus. The path of the proton has a radius of curvature equal to R p and the path of the 7 Li nucleus has a radius of curvature equal to R Li . The ratio R p / R Li is closest to ( a ) 3/1, ( b ) 1/3, ( c ) 1/7, (
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Chap 26 SM - Chapter 26 The Magnetic Field Conceptual...

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