1. Draw in the magnetic field inside each box that would be capable of deflecting the particle along the path shown in each diagram.
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1 Charged Particles in Magnetic Fields 1. Draw in the magnetic field inside each box that would be capable of deflecting the particle along the path shown in each diagram. a b c d 2. a. Three particles with similar masses all pass through a uniform magnetic field with the same velocity. The path each particle took through the field is shown below. Compare the charges of particle A B and C. A B b. If, in the diagram above, particle A and C had the same magnitude of charge (but opposite in sign), what other properties of the two particles could cause the different paths? C
2 3. An is moving through a magnetic field with a density of T at a speed of 4.65 x 10 4 ms -1. A a. What is the magnitude of the force acting on the while it is in the field? b. What direction is the force acting on the at position A, just as the enters the field. c. Describe how the force acting on the at position A would be affected by changing the following properties of the of the field it is passing through: i. Electron is positively charged ii. Electron travels twice as fast iii. Electron has twice the mass iv. Magnetic flux density is halved v. Magnetic flux is doubled. vi. Magnetic flux is redirected to point from left to right vii. Magnetic flux is redirected to point up the page d. What radius of curvature would the follow while in this field?
3 4. A mass spectrometer is a device that is used to help determine the composition of unknown samples by detecting the mass of atoms that make up the sample. One type of mass spectrometer releases ions from the sample either through heat or an gun; these ions are then accelerated up to the same speed. The ions pass through a variable magnetic field and a detector is placed at the end of the path which will pick up any ions that make it through the curved path. a. What is the purpose of the electromagnets in a mass spectrometer? b. The green line represents one type of ion from the sample which the detector picks up. What can you say about the properties of the blue and yellow ions that were also released by the sample. Assume all ions released from the sample have a single positive charge. c. What changes need to be made to the mass spectrometer to ensure all positive ions released from the sample are detected? d. How could you calibrate the mass spectrometer to detect any negative ions that were released from the sample? e. A lithium ion (+1 charge) has a mass of 1.15 x kg and after being released from the sample is accelerated up to 8.56 x 10 4 ms -1. If the mass spectrometer curved path has a radius of 1.20 m, what is the required magnetic flux density needed to detect these ions?
4 5. Another design of mass spectrometer does not use a variable magnetic field. Ions are shot into the field at a specific velocity but the detector is widened and is sensitive enough to pick up where the ions impact the detector. Sample Accelerated ion beam Detector Panel M1 M2 a. Are the ions released by the sample positive or negative? b. Which ion, M1 or M2 would have the greater mass? Justify your answer with relevant formula. c. Two ions of equal charge are detected on the detector panel. Ion M1 was detected 46.0 cm away from where the beam entered the field while ion M2 was detected 58.0 cm from the beam's entry point. How heavy is the heavier ion compared to the lighter ion? d. Which of the following statements is false. Justify your response. i. The kinetic energy of the ion is constant within the magnetic field ii. The work done by the magnetic field on the ion increases with ion mass iii. The acceleration of the ion is not constant within the magnetic field
5 Solutions 1. a b c d a. Particle A has a negative charge. Particle B has no charge. Particle C has a positive charge and a larger charge than A to cause a sharper deflection. b. If A travelled faster than C or A had a larger mass that C could cause particle A to follow a larger radius path. c. d. Down (as determined by the left hand rule) e. i. Force would be up ii. Force would double iii. Force is unchanged iv. Force is halved v. Force is doubled vi. Force is zero vii. Force would be into the page f. Centripetal force = Magnetic force 4. a. To cause the ions to deflect around the curve in the mass spectrometer. b. The yellow ion did not deflect enough around the curve so its mass is heavier than the green ion. The blue ion is lighter than the green ion as it deflected more.
6 5. c. By increasing the magnetic flux density produced by the electromagnets steadily, then all ions will have a chance to be picked up by the detector. d. Reverse the direction of the magnetic field. e. a. Positive as determined by the right hand rule. b. Both particles are undergoing circular motion and thus have a centripetal force given by. The centripetal force is supplied by the magnetic force which is determined by. The size of the magnetic force does not depend on mass so both particles experience the same centripetal force. Therefore the particle with the larger radius also has the larger mass. Particle M2 has more mass. c. The force acting on both ions is the same. Mass of M2 is 1.26 times greater than the mass of M1. d. Statement ii. Is false. A magnetic field does no work on a charged particle because the force is perpendicular to the velocity. The particle energy does not increase. Statement i. is fine as the speed of the particle is constant, hence it has a constant kinetic energy. Statement iii. Is fine as the direction of the acceleration is changing as it is always perpendicular to the current velocity.
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