Sierzega: Magnetism 5 Solutions. Practice Problems

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Hillary Hubbard
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1 Practice Problems 5.1 Represent and reason Two wires are parallel to each other. Wire 1 has electric current going into the page and wire 2 has electric current coming out of the page. Fill in the table that follows to emphasize the importance of choosing a source of a field and a system on which the field exerts a force. 5.2 Represent and reason An electric current travels through a horizontal bar that hangs from two thin side wires (see the side view at the right). In what direction should an external magnetic field point so that the magnetic force that the magnetic field exerts on the bar helps support the bar? Explain. The magnetic field created by the segment of wire parallel to the rod will exert a force down the rod. An external magnetic field would have to point out of the page through the bar such that the force is exerted up.

2 5.3 Evaluate the solution The problem: You are playing a video air hockey game in which a hockey puck of mass m with electric charge +q leaves a velocity selector traveling at speed v on a horizontal frictionless surface. You are to write an expression for the magnitude B of a magnetic field and decide on its direction so that it bends the puck in a curving half circle (toward the bottom of the screen) and it hits a target a distance 2R below the place the puck left the velocity selector. Solution: The situation is pictured at the right, along with a free-body diagram for the puck as seen in the plane of its motion at the instant the puck has reached the halfway point around the half circle. The acceleration direction is indicated. Mathematical Representation Top view Front view F radial = mv 2 /R or qvb sin 90 0 = mv 2 /R. Velocity selector y F S on P Consequently, B = mv 2 /qr and the field points to the left. F B on P x (a) Identify any missing elements or errors in the solution. The magnetic field direction.. Target F E on P A final expression. (b) Provide a corrected solution or missing elements if you find errors. Magnetic field is out of the page. B = mv/qr 5.4 A duck accumulates a positive charge of 3.0 x 10-8 C while flying north at speed 18 m/s. Earth's magnetic field at the duck's location has a magnitude of 5.3 x 10-5 T and points in a direction 62 0 below a horizontal line pointing north. Determine the magnitude and direction of the force exerted by Earth s magnetic field on the duck. F = qvbsin = (3.0 x 10-8 C)(18 m/s)(5.3 x 10-5 T)sin(90+62) = 1.34 x N

3 5.5 Regular problem What happens to a cosmic-ray proton flying into the Earth s atmosphere at a speed of about 10 7 m/s? The magnitude of the Earth s B field is approximately 5 x 10-5 T. The mass m of a proton is approximately kg. Consider three cases: The proton enters the Earth s atmosphere parallel to the B field, perpendicular to the field, and at a 30 0 angle relative to the field.

5.6 Reason Suppose that the rail for a train had an electric current traveling through it and that the train had a large coil such as shown at the right.

4 5.6 Reason Suppose that the rail for a train had an electric current traveling through it and that the train had a large coil such as shown at the right. Can the magnetic field produced by the rail exert a magnetic force on the train that helps support it like magnetic levitation? Explain. Hint: The magnetic field strength decreases with distance from the current-carrying wire. If the current in the rail is traveling in the opposite direction as the train pictured above then the magnetic field will exert a net force on the train that is upwards because the magnitude of the magnetic field would decrease as you get further from the rails. 5.7 Evaluate You work in the complaint office at General Motors. A customer makes a complaint. Fill in the table that follows to describe the process in other ways and decide how you, an employee in the complaint office, will respond. A customer says that while driving through the Earth s magnetic field, a potential difference was developed from one end of her car to the other. The car discharged, causing her to lose control and run off the highway into a ditch. Decide the action you should take. Be sure to use your physics knowledge to help complete the recommendation people have much more confidence in decisions based on physics, don t they? a) Sketch the situation.

5 b) Construct a physical representation (force diagrams, magnetic field diagram, etc). c) Write a mathematical representation. d) Evaluate the argument and provide a recommendation. This is too much charge to put into one place so the customer must think of another excuse for driving off the road. 5.8 Represent and reason The speed of blood flow in an artery can be measured using our knowledge of a magnetic field and an electric field. The process is described below in words. Represent the process in other ways. Positive and negative ions move with blood through a magnetic field in an artery that is perpendicular to the blood s velocity. The magnetic force causes some positive ions to accumulate on one wall of the artery and negative ions on the other wall. This charge separation causes an E field that opposes further charge separation. Derive an expression for the speed of the blood in terms of the electric and magnetic fields. a) Draw a sketch. b) Draw a physical representation.

6 c) Write a mathematical representation.

2. Draw the Magnetic Field lines created by the below two bar magnets. Homework 3. Draw the Magnetic Field lines created by the below bar magnets.

Chapter Problems Magnetic Fields 1. Draw the Magnetic Field lines created by the below bar magnet. S N 2. Draw the Magnetic Field lines created by the below two bar magnets S N N S 3. Draw the Magnetic