Electromagnetic Induction


 Isaac Booker
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1 Electromagnetic Induction Name Section Theory Electromagnetic induction employs the concept magnetic flux. Consider a conducting loop of area A in a magnetic field with magnitude B. The flux Φ is proportional to the number of field lines passing through the loop. Φ = BA cos θ (1) The cosine term in Equation 1 arises from the fact that the number of field lines passing through the loop will change depending on the orientation of the loop relative to the field. The direction of A is taken to be normal to the plane of the loop, as shown in Figure 1. Figure 1: Magnetic Flux The angle θ is the angle between A and B; intuitively, this makes sense. If B and A are parallel (θ = 0 ) then cos θ = 1 and the flux is maximum through A. If B and A are perpendicular (θ = 90 ) then cos θ = 0 and the flux is 0. In general, what Equation 1 gives is the product of A and the component of B parallel to A (perpendicular to the plane of the loop). It was Faraday who first concluded that the emf E induced in a conducting loop is dependent upon the time rate of change of the magnetic flux through the loop. E = Φ t (2) This is known as Faraday s law of induction. The minus sign is an indication of the polarity of the induced emf. If we consider the current produced by this emf and its effect, then 1
2 An induced emf generates a current whose magnetic field opposes the change in flux that produced it. This is known as Lenz s law, and arises from the conservation of energy. Suppose that the induced current produced a magnetic field that added to the original field. This would increase the flux through the loop, which would give rise to a greater current, which would then produce an even greater flux, produce an even greater current, and so on. In physics, you can t get something for nothing! Apparatus Power supply, Galvanometer, Wires, Solenoid, Bar magnet, Decade resistance box, Switch, Magnetic compass. Procedure In this experiment you will use a solenoid as the conducting loop; remember that a solenoid is a series of conducting loops arranged cylindrically. The flux, hence the induced emf, is proportional to the number of loops (turns) N so that Faraday s law becomes E = N Φ t (3) The Galvanometer A galvanometer is essentially an ammeter which shows the magnitude and direction of the current flowing through it. It uses some of the same principles we are studying here, and is the basis for all analog ammeters and voltmeters. However, these require the addition of an appropriate series or parallel resistance, since the maximum current that the galvanometer can handle in either direction is only 500µA (500x10 6 A). Care must be exercised at all times to ensure that you do not send more current than this through it. 5V DC I Decade Galvanometer Since the rules for electricity and magnetism are based on positive test charges and the flow of conventional current (positive charge), we need to know how the galvanometer responds. Put the decade box, galvanometer, and switch in a series circuit with the power supply (COM, +5V) as shown above. [Note: If your galvanometer has (+) and () connections, disregard these 1  they only confuse the issue.] Use Ohm s Law to calculate the resistance needed in the circuit for this fullscale this current, placing the value in Table 1. Set a resistance 20% higher than this on the decade box and have your circuit checked by the lab instructor before proceeding. 1 They are unnecessary in my opinion, as the galvanometer needle deflects in both directions. 2
3 Potential of power supply (V) 5.0 Fullscale galvanometer current (A) 500x10 6 Resistance for circuit (Ω) 20% higher resistance (Ω) Table 1: Circuit Resistance Conventional current is the flow of positive charge around a circuit from the (+) side of the potential to the () side. Follow the connections from the (+) side of the power supply around the circuit and through the galvanometer. Throw the switch and note which direction (left or right) the needle on the galvanometer deflects. Is the deflection of the galvanometer needle in the same direction as the flow of conventional current through the galvanometer or in the opposite direction of the flow of conventional current through it? The Electromagnet Disassemble the previous circuit. We need a consistent orientation for the remainder of the experiment, so proceed as follows: Place the solenoid on the table in front of you such that you are perpendicular to its axis; i.e., you will be looking at the coils of the solenoid rather than through it. Turn, if necessary, such that the connections on the solenoid are at the top rear of the solenoid from your vantage point. Place the power supply behind the solenoid and connect it (COM, +5V) to the solenoid. Hold the compass at the left end of the solenoid, turn on the power supply, and note what happens to the compass needle. Turn off the power supply and repeat with the compass at the right end of the solenoid. Turn off the power supply, switch the leads, and repeat. When conventional current flows through the solenoid from the left side to the right side, which end of the solenoid is the N magnetic pole? S magnetic pole? What about when conventional current flows through the solenoid from the right side to the left side  which end of the solenoid is N? S? This should help you verify your diagrams in the next procedure. 3
4 Induction (Coil and Magnet) Replace the power supply with the galvanometer this arrangement shown in Figure 2. Figure 2: The Solenoid On a separate sheet of paper, provide a series of sketches similar to Figure 2 with the results of the following investigations: 1. N end of the magnet inserted into right end of solenoid 2. N end of magnet removed from the right end of the solenoid 3. S end of the magnet inserted into right end of solenoid 4. S end of magnet removed from the right end of the solenoid 5. N end of the magnet inserted into left end of solenoid 6. N end of magnet removed from the left end of the solenoid 7. S end of the magnet inserted into left end of solenoid 8. S end of magnet removed from the left end of the solenoid On each, indicate the direction of the needle deflection as shown on the galvanometer, the direction of the induced conventional current through the solenoid, and the direction of the induced magnetic field in the solenoid. In order to do this, you will need to know how the coils are wound around the solenoid. If viewed from either end; i.e., when looking through it, the coils are clockwise from your end to the far end. The observations in your diagrams should agree with predictions made with the righthand rule. In the above situations, the magnet was moved into and out of a stationary solenoid. What would happen if the solenoid was moved toward and away from a stationary magnet? Hold the magnet stationary on the right side of the solenoid (N end of the magnet closest to the solenoid) and move the solenoid to the right until the N end of the magnet is inside the solenoid. After this, move the solenoid to the left until the magnet is again outside the solenoid. Were your results analogous to situations 1 and 2 above? Would you expect similar results in 38? Why or why not? 4
5 What is induced in the solenoid if there is no relative motion between the magnet and solenoid; i.e., the magnet is held stationary inside or outside the solenoid? See if you can induce a current in the solenoid in any other way not already investigated. observations here. Record your 5
6 PreLab: Electromagnetic Induction Name Section Answer the questions at the bottom of this sheet, below the line  continue on the back if you need more room. Any calculations should be shown in full. 1. What is Faraday s law of induction? 2. What is Lenz s law? 3. What is conventional current? 6
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