One important aspect of magnetism and electricity is induction. Experiments regarding induction have begun since 1800s, starting with the help of Michael Faraday. Through these experiments, concepts such as an induced current and electromotive force (EMF) were born. The experiments showed the induced current is produced by moving a coil around a stationary magnet; while induced EMF is the corresponding electromotive force due to this action. Induction occurs because of a changing magnetic flux within the loop. Faraday’s law describes this, stating that the induced EMF in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. Mathematically, it is stated as: = −
Φ
(8.1)
Another important law in induction inducti on is Lenz’s law, which states that the direction of any magnetic induction effect is oriented in such a way that it opposes the cause of the effect. This, too, may be due to the changing flux throughout the stationary circuit, due to the magnetic field. The objectives of this experiment, then, are to demonstrate Faraday’s law and Lenz’s law using an electromagnetic setup, determine the effect of rate of motion of a magnet through a coil on the induced current, and lastly, determine the direction induced EMF when the magnet passes through the coil. Methodology In the first part of the experiment, EMF was induced in a solenoid with the use of magnet. The voltmeter interfaced with LabQuest was connected to the terminals of the secondary solenoid. The magnet was then dropped with north pole as its bottom through the solenoid. The voltage as the magnet moves through the solenoid was afterwards recorded. In the second part of the experiment, the current was induced in a solenoid with the use of magnet. The galvanometer was connected to the terminals of the secondary solenoid which is characterized by larger coil with greater number of turns. The magnet was then placed inside the solenoid. The magnitude and direction of the galvanometer reading was afterwards recorded. It was repeated using different rate of magnet movement and the other step was with the south pole facing the solenoid. In the third part of the experiment, current was induced in a solenoid with the use of a power supply. The length of the primary solenoid, the smaller one, was measured and recorded. The primary solenoid was then inserted into the secondary solenoid while the secondary solenoid was connected to the galvanometer. Afterwards, the primary solenoid was connected to the power supply. The power supply was then turned on and the magnitude and direction of the galvanometer deflection was recorded. The power supply was then turned off and the magnitude and direction of the galvanometer galvanometer deflection was recorded as well. On the other hand, an aluminum rod was placed inside the primary solenoid. Same steps upon turning the power supply on and off were done. Same procedure was then performed using an iron rod. The power supply was turned off after the induced current was measured. With the iron r od inside the primary solenoid, the primary solenoid was withdrawn one centimeter centimeter from the secondary solenoid and the length of the primary solenoid that is still inside the secondary solenoid was recorded. This step will be done until until the whole whole primary primary solenoid was was outside the secondary secondary solenoid. solenoid.
The last part of the experiment was about Lenz’s law and Eddy current. The given aluminum plates were positioned between the magnets and was let to swing freely. This process was repeated for the other plates.
RESULTS AND DISCUSSION The first part of the experiment involved the induction of current in a solenoid through a magnet. While the magnet was stationary, the reading remained at zero. This could be explained by the lack of magnetic flux on the solenoid’s wire loops, thus no induced current. Another observation showed that the faster the motion of the magnet inside the solenoid, the higher the received reading. Faraday’s law explains this, as it states that the induced EMF is equal to the rate of change of the flux. Thus, the higher the EMF induced, the higher current induced, and so, the higher magnitude on the reading. If more loops were added on the solenoid, the induced EMF will increase, as more loops will experience the change in magnetic flux. When the poles were reversed, in other words, the magnet was moved through the opposite pole, the induced current was the negative value from the former pole. This is because the direction of their magnetic field are opposite of each other; however, the magnitude stays the same. To resist the change in magnetic flux, a current would have to be induced to create a magnetic field that opposes the change. Since the value of change in magnetic flux is negative, the induced current would also be in the opposite direction. Another observation is that the magnetic field intensity is the strongest at the magnet’s poles. When one of the poles was moved toward the coil, the magnetic flux increased; and when this was moved away, the magnetic flux decreased. The same observation can be said for the opposite pole, although whatever the value in the previous pole would be the in the opposite direction for this pole. Furthermore, comparing the values of the induced current and EMF, the values of the two were the negative of the values of the result when the poles were being moved toward the solenoid. The second experiment involved inducing current by turning a circuit on and off. When a switch is turned on, current does not immediately jump to the maximum value. As such, when the circuit increases from zero to some value, magnetic fields surrounding the wires pass through a loop and create a magnetic flux. This then is a magnetic flux in the loop. As the circuit increases, the flux increases, too, creating an induced EMF, which results to an induced current in the loop. It should be remembered that induced EMF opposes its cause, which in this experiment is the power supply. The opposite occurs when turning the circuit off, which instead gives an opposite sign in the direction of maximum current. With the formula for inductance of a solenoid:
Changing the core material of the primary solenoid changes the inductance of the loop, which will, in turn, change the induced EMF and current in the loop. This can be seen in the formula: emf = -L (di/dt)
(8.2)
From data gathered, it is shown that current increases from air, to the aluminum rod, to the iron rod. Thus, it can be said that the magnetic permeability is also increasing because the magnetic permeability of iron is higher than aluminum. Two close solenoids will have their magnetic field lines pass each other; this is due to the fact that the magnetic flux causes induction on the other, and since both of them have magnetic flux, both of them will also cause induction. This occurrence is called mutual inductance. However, mutual inductance focuses more on the geometry of the circuits and their spacing with respect to each other. Moving farther apart, they have less magnetic field lines and less mutual inductance. Also, moving the primary solenoid from the secondary solenoid lessens the mutual inductance, causing a smaller induced EMG and thus a less induced current. The third part of an experiment used three aluminum pendula, namely a fork, a spoon, and a strain. These three were passes between the gap of a permanent magnet. From the observations recorded, it was seen that the fork swung the longest, with an average of 18.33 swings and 7.46 swing duration. On the other hand, the spoon swung the fastest, with an average of 5 swings and only 2.24 s of swing duration. This may be credited to the fact that both spoon and strain are solid plates, thereby stopping easily at the magnet’s gap. However, with the forks, its slotted plates only swing slightly as they pass through the magnetic field. Aluminum plates oscillate as they are attracted to a magnetic field; thus, the more magnetic fields passed, the faster the oscillation. This phenomenon springs up from induced eddy currents. It has been said before that Lenz’s law stated that c hanging magnetic flux induces currents that tend to oppose the change in flux. These currents produce induced magnetic field that oppose the external field the created the currents. It is due to the interaction of the induced and external magnetic fields that the pendula stop. If large induced magnetic fields were present, large induced currents are produced, leading to a slower swing. In the slotted plates of a fork, however, the induced eddy currents are broken up by slots, and the slotted plate passes through the magnetic field with only slight slowing. Thus, it can be said that the shapes of the pendula affected their swings.
Eddy currents are present in conductors, and move through uniform magnetic fields. Thus, changing the material of the pendulum may affect the ability of the magnetic field to stop swinging.
CONCLUSION In this experiment, Faraday’s and Lenz’s law were proved through the observation of the behavior of induced EMF and induced current when a magnet with a certain pole facing the solenoid was the dropped. From here, it can be said that as the change in magnetic flux and the velocity of the magnet increases, the magnitude of the induced current also increases and vice versa. The magnetic permeability of objects were also observed: the higher permeability of the core object in a solenoid, the greatest the induced EMF and current. Lastly, the more compact a conductor that is passing through a magnetic field, the greater the effect of the eddy current and the faster the time it will stop the conductor from moving.
