Can a Magnetic Field Produce a Current?

Transcription

1 Can a Magnetic Field Produce a Current? In our study of magnetism we learned that an electric current through a wire, or moving electrically charged objects, produces a magnetic field. Could the reverse happen? Could a magnetic field produce a current? 1.1 Observe and find a pattern The table describes five experiments involving a galvanometer, a bar magnet, and a coil. The outcomes of the experiments are included. Observational Experiment Analysis a. You hold a magnet motionless in front of a coil. The galvanometer reads zero. There is no current through the coil. b. You move the magnet toward the coil or move the coil toward the magnet. The galvanometer needle moves to the right, inducing a current through the coil. c. You move the magnet away from the coil or move the coil away from the magnet. The galvanometer needle moves to the left, indicating a current through the coil but opposite the direction in the last experiment. d. You turn the magnet 90 so that the poles are now perpendicular to their previous position. The galvanometer registers a current while the magnet is turning e. You collapse the sides of the coil together so it s opening becomes very small. You pull open the sides of the collapsed coil so the area becomes large again. In both cases, the galvanometer registers a current while the coil s area is changing, but the direction is different in each case. f. Patterns Although no battery was used, an electric current was induced in the coil when the magnet and coil moved toward or away from each other. Current was also induced when the coil s orientation relative to the magnet or the area of the coil changed.

2 1.2 Predict and test The following experiment uses two coils. Coil 1 on the bottom is connected to a battery and has a switch to turn the current through coil 1 on and off. When the switch is open, there is no current in coil 1. When the switch is closed, the current in coil 1 produces a magnetic field whose B-field lines pass through coil 2 s area. For each of the experiments we will use our explanation to predict whether or not there should be an induced electric current in coil 2. Testing Experiment Experiment 1: The switch in the circuit for coil 1 is open. There is no current in coil 1. Is there any current in coil 2? Experiment 2: You close the switch in the circuit for coil 1. While the switch is being closed, the current in coil 1 increases rapidly from zero to a steady final value. Is there any current in coil 2 while the switch is being closed? Experiment 3: You keep the switch in the circuit for coil 1 closed. The current in coil 1 has a steady value, Is there current in coil 2? Experiment 4: You open the switch again. Is there any current in coil 2 while the switch is being opened? Will a current be induced in coil 2? Based on our explanation: Induced current is due to magnetic force exerted on moving charged particles. There is no current in coil 1, thus there is no magnetic field at coil 2. Neither coil is moving. No current will be induced in coil 2. Neither coil is moving thus no current will be induced in coil 2. Neither coil is moving. Thus no current will be induced in coil 2. Neither coil is moving. Thus no current will be induced in coil 2. Outcome The galvanometer registers no current in coil 2. Just as the switch closes, the galvanometer needle briefly moves to the left and then returns to vertical, indicating a brief induced current in coil 2. The galvanometer registers no current in coil 2. Just as the switch opens, the galvanometer needle briefly moves to the right (opposite the direction in experiment 2), then returns to the vertical, indicating a brief induced current in coil 2. Conclusion The predictions based on our explanation did not match the outcomes in 2 of the 4 experiments. Motion is not necessary to have an induced current. In contrast, when the number of B-field lines through a coil s area changes, there is an induced current in that coil. This phenomenon of inducing a current using a changing B-field is called electromagnetic induction.

3 1.3 Observe and find a pattern The table that follows describes five new experiments using a galvanometer, a bar magnet, and a coil. The outcomes of the experiments are included. Experiment Illustration Outcome 1. Position a magnet perpendicular to the coil and move it slowly toward the coil. Repeat the experiment, moving the magnet quickly. 2. Position a small magnet perpendicular to the coil and move it slowly toward the coil. Repeat the experiment using a bigger magnet. 3. Move a magnet perpendicular to the coil. Then move it so that it makes an angle with the plane of the coil. Keep the speed the same. 4. Make a small coil and a large coil. Move the magnet toward each. The quicker the magnet s motion, the stronger the induced current. The bigger magnet induces a bigger current than the small magnet when they move at the same speed with respect to the coil. When the magnet moves perpendicular to the coil, the biggest current is induced. A stronger current is induced in the larger coil. 5. Make two coils of the same area, one with two turns and one with ten turns. Move the magnet toward each. A stronger current is induced in the coil with more turns. Devise in words a rule that relates the magnitude of the induced current to various properties of the magnet, its motion, and properties of the coil. An electric current is induced when the number of B-field lines through the coil s area changes. This occurred when: The strength of the B-field in the vicinity of the coil changed, or The area of the coil changed, or The orientation of the B-field relative to the coil changed. Magnetic Flux (: a physical quantity for the number of B-field lines through a coil s area. How does Magnetic Flux ( depend on B-field? On area? How do we include the dependence of the orientation of the loop relative to the B-field lines?

4 Did you know? Magnetic Flux (The magnetic flux through a region of area A is = AB cos Where B is the magnitude of the uniform magnetic field throughout the area and is the angle between the direction of the B field and a normal vector perpendicular to the area. The SI unit of magnetic flux is the unit of the magnetic field (T) times the unit of area (m 2 ), or T*m 2. This unit is also known as the weber (Wb). Direction of the Induced Current 1.4 Observe and find a pattern The table that follows repeats three earlier experiments that used a galvanometer, a bar magnet, and a coil and in which a current was induced. The direction of the induced current is shown in the illustrations. Experiment Draw B field vectors caused by the moving magnet. Indicate whether the field vectors through the coil are decreasing or increasing. Draw B ind field vectors due to the induced current. The coil area is collapsing. The coil expands (a) Use the data in the table above to devise a rule relating the direction of the induced current in the coil and the change of external magnetic flux through it. Fill in the table on the following page. Hint: (1) Draw the B field vectors of the moving magnet and make a note of whether the flux due to the magnet is increasing or decreasing though the coil. (2) Then draw B ind vectors as a result of the induced electric current. Compare the direction of B ind vectors to the B field vectors of the moving magnet (3) when the flux through the coil increases and (4) when the flux decreases.

5 Direction of B-field ( or ) Flux (Increasing or Decreasing) Induced Current (Clockwise or counterclockwise) Direction of Resulting Current s B-field ( or ) (b) How does the direction of the induced current in a coil relate to the change of external magnetic flux through it? Did you know? Lenz s law The direction of the induced current in a coil is such that its B-field opposes the change in the magnetic flux through the coil s area produced by other objects. If the magnetic flux through the coil is increasing, the direction of the induced current s B-field leads to a decrease in the flux. If the magnetic flux through the coil is decreasing, the direction of the induced current s B-field leads to an increase in the flux.

6 1.5 Reason For each situation shown in the table that follows, use the rules devised and tested in the previous handout to predict if a current is induced through the resistor attached to the loop. If a current is induced, indicate the direction of that induced current. Experiment (a) The loop is perpendicular to the page. Predict if a current is induced; explain your prediction. If you predict that a current is induced, what is the direction of the current? (b) The loop is perpendicular to page and the magnet turns 90 o. (c) The loop and magnet are in the plane of the page. (d)the loop, perpendicular to page, is pulled upward so that it collapses. (e) The switch in the left circuit is closed and the current increases abruptly.

7 (f) A steady current flows in the left circuit. (g) The circuit on left is rotated 90 o about the dotted line. (h) The switch in the left circuit is opened and the current decreases abruptly.