Lesson 12: Magnetic Forces and Circular Motion!


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1 Lesson 12: Magnetic Forces and Circular Motion If a magnet is placed in a magnetic field, it will experience a force. Types of magnets: Direction of the force on a permanent magnet: Direction of the force on an electromagnet: Third Hand Rule: Left Hand: Right Hand: Thumb: Fingers: Palm: Example 1: For a magnetic field into the page, what is the direction of the force on a proton initially travelling to the left?
2 Example 2: A current carrying wire is placed in a magnetic field directed upwards. What is the direction of the magnetic force on the top section of the wire? Example 3: A proton and an electron are place into a magnetic field directed into the page. Particle A experiences an upward force and Particle B experiences a downward force. Which particle is the proton? Force on a charged particle traveling in a magnetic field: Direction = third hand rule Magnitude: Note: This formula only works if the velocity is perpendicular to magnetic field If velocity is not perpendicular, you must calculate the perpendicular component first and use it instead
3 Example 4: An electron has an initial velocity of 9.1x104 m/s [left] when it enters a magnetic field of 1.1 x102 T [into the page]. What is the force on the electron as it enters the field? Example 5: An electron has an initial velocity of 1.9x105 m/s [20o S of W] when it enters a magnetic field of 2.4 x103 T [N]. What is the force on the electron as it enters the field? Example 6: An electron has an initial velocity of 1.5x103 m/s [S] when it enters a magnetic field of 1.1 x105 T [S]. What is the force on the electron as it enters the field?
4 Magnetic Forces and Circular Motion When a moving charged particle enters a magnetic field, it experiences a force perpendicular to its motion. This causes the particle to travel in a circular path Eventually, the particle will continue to travel in the original direction of motion, but in a spiralled path Since the circular motion of the particle is caused by the magnetic force:
5 Example 7: A particle with a charge equal to the elementary charge enters a magnetic field of 14 T with a speed of 2.3x10 6 m/s. The particle moves in a circular path of radius 935 nm. Is the particle a proton or an electron? Example 8: An electron is accelerated from rest using a voltage of 200 V before it enters a magnetic field of 0.15 T perpendicular to that field. What is the radius of the electron s path? The Northern Lights: When charged particles from the sun (solar wind) spiral along Earth s magnetic field, the result is the northern lights (also called Aurora Borealis)
6 Practice Problems: 1. For the following diagram, what is the direction of the deflecting force if the particle is: A. B. an alpha particle an electron S N 2. Trace out the path of the positive particle in the indicated magnetic field 3. Three particles move through a constant magnetic field and follow the paths shown in the drawing. Determine whether each particle is positive, negative or neutral. Give reasons for your answers Three particles have identical charges and masses. They enter a constant magnetic field and follow the paths shown in the picture. Which particle is moving fastest, which is moving slowest? Justify your answer. Calculate the magnitude and direction of the magnetic force on an electron travelling north at a speed of 3.52 x 105 m/s through a vertically upward magnetic field of 2.80 x 101 T. [1.58 x N [W]]. An electron experiences an upward force of 7.1 x N when it is travelling 2.7 x 105 m/s south through a magnetic field. What is the magnitude and direction of the magnetic field? [1.6 T [W]]
7 7. An electron is accelerated from rest by a potential difference of 1.70 x 10 3 V, and then enters a magnetic field of 2.50 x 101 T moving perpendicular to it. What is the magnitude of the magnetic force acting on the electron? [9.77 x N] 8. Calculate the downward acceleration on an electron that is travelling horizontally at a speed of 6.20 x 10 5 m/s perpendicular to a horizontal magnetic field of 2.30 x 101 T. [2.50 x m/s 2 ] 9. What deflecting force is exerted on a charge of 40 µc moving at 15 cm/s at 30 o to the magnetic field with a strength of 0.025T? (7.5 x 108 N) 10. What happens to the motion of an electron that is moving in the same direction as the magnetic field which it enters? 11. What is the deflecting force on an alpha particle moving at 1.0% of the speed of light directly across a magnetic field whose flux density is T? (2.9 x N) 12. From what direction must charged particles approach the Earth in order to be unaffected by the Earth's magnetic field? 13. An electron and a proton, each with a speed of 1.2 x 10 2 m/s enter a magnetic field of T at 90 o to the field as shown below. N S A. Calculate the force on each particle. (3.84 x N) B. Calculate the acceleration experienced by each particle. (4.2 x m/s 2 out of page, 2.3 x 10 7 m/s 2 into page) 14. Calculate the magnitude and direction of the magnetic force on an alpha particle moving south at a speed of 7.40 x 10 4 m/s through a vertically upward magnetic field of 5.50 T. (1.30 x N west) 15. Solar wind is a thin hot gas given off by the sun in all directions. Some of the charged particles enter the magnetic field of the Earth and can experience a magnetic force. Suppose some charged particles traveling at 9.0 x 10 6 m/s encounter the Earth's magnetic field at an angle of 90 o where the magnitude of the field is 1.2 x 107 T. Find the radius of the circular path on which the particle would move it were (a) an electron and (b) a proton. (4.3 x 10 2 m, 7.8 x 10 5 m)
8 16. The drawing shows a top view of four interconnected chambers. A negative charge is fired into chamber 1. By turning on separate magnetic fields in each chamber, the charge can be made to exit chamber 4. (a) Describe how the magnetic field in each chamber should be directed. (b) If the speed of the particle is v when it enters chamber 1, what is its speed when it exits chamber 4? Explain. 17. An ionized helium atom has a mass of 6.6 x kg, a speed of 4.4 x 10 5 m/s and moves perpendicular to a 0.75 T magnetic field in a circular path with a radius of m. What is the magnitude of the charge on the helium nucleus? (3.2 x C) 18. A velocity selector is a device for measuring the speed of a charged particle. The drawing shows that a velocity selector consists of a cylindrical tube located with a constant magnetic field B. Inside the tube there is a parallel plate system that produces a uniform electric field E. A positive charge enters the left end of the tube. If E and B are properly adjusted, the charge will exit the right side of the tube undeflected. For such a situation, derive an expression for the speed (v) of the particle in terms of B and E. 19. An ion source in a mass spectrometer produces deuterons (a deuteron has twice the mass of a proton, but the same charge). Each deuteron is accelerated from rest through a potential difference of 2000 V after which it enters a T magnetic field. Find the radius of the circular path. ( m) 20. Calculate the magnitude and direction of the magnetic force on an alpha particle moving south at a speed of 7.40 x 10 4 m/s through a vertically upward magnetic field of 5.50 T. (1.30 x N west) 21. A proton moves in a circle in a uniform 1.8 T magnetic field. If its radius of curvature is 3.0 cm, what is its velocity? [5.2 x 10 6 m/s] 22. A charged particle (q = +e) is moving at 1.9 x 10 4 m/s at right angles to a uniform magnetic field of 1.0 x 103 T. If the radius of curvature of its path is 0.40 m, what is its mass? [3.4 x kg] 23. An electron, shot at right angles into a uniform magnetic field of 2.0 x 103 T, experiences a force of 2.6 x N. With what velocity is it moving? [8.1 x 10 5 m/s] 24. A horizontal eastwest wire carries a current flowing west. A beam of positive alpha particles is shot directly down at the wire from above. In what direction will they be deflected?
9 25. A single ionized uranium ion of mass 3.9 x kg is accelerated through a potential difference of 1.0 x 10 5 V. a) What is its maximum velocity? [2.9 x 10 5 m/s] b) What is the radius of the path it would take if injected at 90 o into 0.10 T uniform magnetic field at this velocity? [7.0 m] *26. An electron, traveling at a speed of 3.62 x 10 6 m/s, enters a magnetic field with a strength of T at an angle of 75 o to the magnetic field lines. when it enters the magnetic field, the electron has a helix spiral (corkscrew) path. What is the distance between the spirals? (8.73 x 104 m) 27. Consider the following diagram that represents an electron moving into the plane of the page. V = 2000 V between charged plates d = m between charged plates B = T The electron enters the electric field, which is perpendicular to the magnetic field, and passes through both fields undeflected. The diagram indicates an electron moving into the page. a). Draw vectors on the diagram to indicate the direction of Fm and Fe on the electron. b). Calculate the speed of the electron. (8.9 x 10 m/s)
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