The principles of electromagnetic induction are applied in many devices and systems, including induction cookers, transformers and wireless energy transfer; however, few data are available on resonance in the electromotive force (EMF) of electromagnetic induction. We studied electromagnetic induction between two circular coils of wire: one is the source coil and the other is the pickup (or induction) coil. The measured EMF versus frequency graphs reveals the existence of a resonance/anti-resonance in the EMF of electromagnetic induction through free space. We found that it is possible to control the system’s resonance and anti-resonance frequencies. In some devices, a desired resonance or antiresonance frequency is achieved by varying the size of the resonator. Here, by contrast, our experimental results show that the system’s resonance and anti-resonance frequencies can be adjusted by varying the distance between the two coils or the number of turns of the induction coil.
Resonance occurs widely in nature and is exploited in many man-made devices. Electric resonance is used in many circuits [1-5]; for example, radio and TV sets use resonance circuits to tune in to stations. In these devices, many frequencies reach the circuit simultaneously through the antenna, but significant current flow is induced only by frequencies at or near the circuit’s resonance frequency. By varying the inductance or capacitance, the device can be tuned to different stations. In physics, resonance is the tendency of a system to oscillate at a greater amplitude at the system’s resonance frequencies than at others. At these frequencies, even small periodic driving forces can produce large amplitude vibrations because the system stores the vibrational energy. In this work, we studied electromagnetic induction between two circular coils of wire: one is the source coil and the other is the pickup (or induction) coil, and report the characteristics of and control over the resonance and anti-resonance in the electromotive force (EMF) of electromagnetic induction through free space.
The experiment was performed based on Faraday’s law:
where and are the EMF induced in the induction coil and the magnetic flux passing through the induction coil, respectively [1,6]. The experimental setup consists of two circular coils of wire composed of an electrically conductive copper wire of cross-sectional radius 0.35 mm tightly wound into a series of loops of 5 - 320 turns, radius 7 cm and height 2 cm, as shown in
over time. Thus, an EMF is induced in the pickup coil. If the magnetic flux passing through the pickup coil is, then the induced EMF is . As increases, increases, and the magnitude of is proportional to the rate at which the magnetic flux changes with time, so that faster changes give a stronger. Here our question is: how does the magnitude of behave as increases, especially in the high frequency range of 10 kHz to a few MHz?
Figures 2(a) and (b) show typical behaviors of 1) the root-mean-square value of of the pickup coil and 2) the phase difference between the applied voltage (to the source coil) and the generated (in the pickup coil), respectively, as a function of the applied frequency (to the source coil). We expected that, according to Faraday’s law and the radiation resistance of the coil, would increase with increasing and then finally attain a new equilibrium, as shown by the black dashed line in
However, the experimental data exhibited a very different behavior, as shown by the red solid circles in
The abrupt change in the phase difference may have been due to motions of the charges in the pickup coil. If the phase difference arose from the acceleration of conducting electrons induced by the electromagnetic radiation (generated from the source coil), the phase difference may be effectively independent of at high frequencies. However, if the phase difference arose from the oscillations in the electric/magnetic dipoles or toroidal dipoles1 [8-14] induced by the electromagnetic radiation, the phase difference would be expected to depend on at high frequencies.
The radiation resistance in a coil with turns composed of an electrically conductive copper wire may be modeled as follows. For a coil of, radius 7 cm and height 2 cm, as used here (see
To determine whether the resonance frequency and
anti-resonance frequency could be adjusted, we examined the influence of three experimental parameters on the and. Figures 3(a)-(c) show graphs of versus for various 1) voltages applied to the source coil (= 2, 6, 10 and 14 V), 2) distances between the two coils (d = 10, 30, 100 and 1000 mm), and 3) numbers of turns of the pickup coil (= 5, 50, 150, 250 and 320), respectively. Figures 4(a)-(c) show variations of and for, and nB, respectively, obtained from
and each show peculiar behavior. The and curves shown in
spectively. According to
We showed experimentally that pickup coils with different resonance/anti-resonance frequencies could be obtained by selecting the appropriate and for a given coil size. These results suggest the possibility of “a wireless power transfer station” that transmits power from a source coil to a large number of pickup coils
through free space. If several pickup coils (with different resonance/anti-resonance frequencies) were positioned around a source coil (i.e., a short-range power networking system), power could be transferred from the source coil to the pickup coils by modulating the rate of change (over time) of the magnetic flux passing through each pickup coil. Wireless power transfer stations that are analogous to radio stations may be realized in the near future to permit everyone to use power anywhere without the need for wired power transmission.
In summary, we have studied the electromagnetic induction between two circular coils of wire and showed clearly the existence of resonance/anti-resonance in EMF of electromagnetic induction through free space. We believe that our results might provide a competitive approach toward the development of high-efficiency systems in devices of induction cookers, electric power transformers, and wireless energy transfer.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number 2012R1A1A 2042743).