Pre-lab Quiz/PHYS 224 Faraday s Law and Dynamo Your name Lab section 1. What do you investigate in this lab? 2. In a dynamo, the coil is wound with N=100 turns of wire and has an area A=0.0001 m 2. The magnetic field is B=0.1 Tesla. If the coil is connected in a circuit with the total resistance R=150 Ω. When the coil rotates from θ=85º to θ=95º, find the amount of charge passing through the circuit during the process. Note: use the unit of radian for θ. (Answer: Q=1.1 10-6 Coulomb)
Lab Report/PHYS 224 Faraday s Law and Dynamo Name Lab section Objective In this lab, you investigate Faraday s Law and measure the induced emf (electromotive force) using a dynamo. Background (A) Faraday s law Figure 1 displays a simple model of dynamo, consisting of a rectangular coil (Coil A) placed in a uniform magnetic field B (in this lab, B is produced by a permanent magnet). The area of the coil is A. n is the normal of the coil (namely, n is perpendicular to the plane of the coil). The angle between B and n is θ. The magnetic flux through the coil is given by BAcos. (1) When the coil rotates around the vertical dashed line (which is perpendicular to both B and n), the magnetic flux changes. Following Faraday s law, an emf is induced in the coil emf BA sin, (2) where is the angular velocity of the coil. If the coil is wound with N turns of wire, every turn attains such an emf. The total emf in the coil is thus emf NBA sin. (3) If the coil is a part of a circuit with the total resistance (including the resistance of the coil) as R, the induced emf produced a current I in the circuit with emf NBA I sin. (4) R R Q Recalling that the current is the rate of the charge passing through the circuit, i.e., I, Equation (4) can be rewritten as Q NBA sin. (5) R In this lab, Coil A will be rotated in steps. For each step, the coil executes a rotation by a small angle θ in a short time period t, during which only transient current is produced during t. According to Equation (5), the amount of charge passing through the coil during t (like a charge pulse ) is emf NBA Q sin. (6) R R Therefore, one can prove Faraday s law by measuring the Q-versus- sin relationship. (B) Using ballistic galvanometer to measure charge pulse In this lab, the ballistic
galvanometer consists of also a moving coil (Coil B) placed in a uniform magnetic field produced by a permanent magnet. When it rotates away from its equilibrium position (for example, by an impulse produced by magnetic force) with a finite angular velocity, Coil B will rotate back and forth around the equilibrium position, behaving like a harmonic oscillation with the maximum rotation angle from the equilibrium position proportional to the initial angular velocity. Only the dissipative forces such air resistance and friction, or an external damping mechanism will slow down or stop the oscillation. For a ballistic galvanometer, the moment of inertia of the coil is so large that the period of its harmonic oscillation is very long. For this lab, we start by setting Coil B at rest at its equilibrium position. To measure the charge pulse Q described in (A), Coil B is connected to Coil A (described in (A)). When charge Q passes through Coil A, it also passes through Coil B, thus inducing a transient current in Coil B. Because Coil B is placed in the uniform magnetic field, the transient current passing through Coil B receives magnetic force. This magnetic force throughout Coil B altogether exerts a magnetic torque on it. Coil B thus acquires a transient angular acceleration, which is proportional to the transient current. At the end of the transient current, Coil B attains a finite angular velocity which is proportional to the total Q. If t (the time duration of the transient current) is much shorter than the period of the harmonic oscillation of Coil B, at the end of the transient current, Coil B is still near its equilibrium position, but now attaining a finite angular velocity proportional to Q. Because of the finite angular velocity, Coil B will oscillate around the equilibrium position and the maximum rotation angle from the equilibrium position is proportional to Q. This rotation angle is read out by the deflection of a needle attached to Coil B. Therefore, the maximum deflection of the needle, A deflection, which can be reached after the transient current will be used to determining Q induced by each step of rotation of Coil A. Therefore, one can prove Faraday s law by measuring the A deflection -versus- sin relationship, which reflects the Q -versus- sin relationship. EXPERIMENT Apparatus The block diagram in Figure 2 schematically displays the set-up used in this lab. The dynamo, the ballistic galvanometer, and the damping key are connected in parallel. However, only when the key is pushed down will the damping key be connected to the ballistic galvanometer. In so doing, Coil B in the ballistic galvanometer quickly stops oscillation and returns to the equilibrium position.
Procedures 1. Set up the circuit (Figure 2) Connect the dynamo, the ballistic galvanometer, and the damping key in parallel. 2. Set up the dynamo In the dynamo, Coil A rotates with a ratchet wheel. The ratchet wheel is attached to the shaft passing through the center of Coil A and is graduated in 10º steps through 360º. The release lever on top of the ratchet wheel has two teeth which can stop the ratchet wheel. When the release lever is flipped (alternately to the left and to the right), the two teeth move by 10º and the ratchet wheel also rotates by 10º. Coil A is actuated by a helical spring which is set by a control lever. The control lever carries a pawl which engages its teeth on the ratchet wheel. Thus, when the ratchet wheel rotates by 10º, the control lever also rotate by 10º. So does Coil A. Using the ratchet wheel, rotate Coil A to the θ=0º position, such that the plane of Coil A is perpendicular to the magnetic field induced by the permanent magnet in the dynamo. Because the magnetic field in the dynamo points along the vertical direction, the plane of Coil A should be horizontal to make θ=0º. Next, lift the control lever and rotate it to the bottom of the ratchet wheel and engage its teeth on the wheel. Use a rubber band to tie the control lever to the top frame of the ratchet wheel and the rubber band should be tightly stretched. 3. Set up the dynamo If the needle of the ballistic galvanometer is not at the central zero reflection position, rotate the dark dial on its top to rotate the needle to the zero deflection position. Push down the damping key long enough to make the needle stop completely at the zero deflection position. Ask your TA to check the set up! 4. Rotating Coil A of the dynamo with θ increasing from 0º to 10º Before each measurement, first check the ballistic galvanometer to make sure that the needle already stops at zero deflection. If not, push down the damping key long enough to make the needle stop completely at zero deflection. Now, flip the release lever on the dynamo. Coil A of the dynamo quickly rotates by 10º, inducing a transient current cause a charge pulse of Q. The transient current drives Coil B in the ballistic galvanometer to rotate. Its maximum rotation angle is indicated by the maximum deflection of the needle, A deflection, which is proportional to Q. Record the corresponding θ and A deflection values in Table 1. 5. Repeat step 4 by rotating Coil A and increasing θ from 10º to 360º, in 10º steps Before each step, check if the rubber band become loose. If so, lift the control lever and rotate it to the bottom of the ratchet wheel and engage its teeth on the wheel. Use rubber bands to tie the control lever to the top frame of the ratchet wheel and the rubber band should be tightly stretched. Caution: do not rotate the ratchet wheel while making this adjustment! Before each step, also check the ballistic galvanometer to make sure the needle is at zero deflection. If not, push down the damping key long enough to bring the needle to stop completely at zero deflection. For each step, record the corresponding values of A deflection values in Table 1. Note: in Table 1 the averaged θ value during each step is used.
TABLE 1 θ (º) sin θ A deflection θ (º) sin θ A deflection 5º 185º 15º 195º 25º 205º 35º 215º 45º 225º 55º 235º 65º 245º 75º 255º 85º 265º 95º 275º 105º 285º 115º 295º 125º 305º 135º 315º 145º 325º 155º 335º 165º 345º 175º 355º Analysis 1. Calculate sinθ for each θ value and record it in Table 1. 2. Because in this lab, θ=10º=0.175 radian is a constant. Plot the A deflection -versus-θ curve. 3. From the curve, find the maximum A deflection value and the corresponding θ values. Record: θ max =
Questions 1. How many θ max angles do you expect for the largest magnitude of A deflection? Explain. 2. Does the angle of θ max correspond to the smallest or the largest magnitude of Q? Explain. 3. Should the A deflection -versus-sinθ curve be a straight line? Why? 4. If the lab is designed such that Coil A of the dynamo is rotated with θ increasing from 0 to 360º, each step with an increment of 20º, will this be a better experiment?