Form Of Magnetic Field Energy example essay topic

My project's goal was to make a metal detector that can successfully detect pieces of metal (actually anything conductive) within a range of 15 cm depending on the object's conductivity and its surface area parallel to the plane of the search coil (and I did it! ). My detector is a simple one with almost no discrimination, which means that it will detects metal objects independent of their chemical composition or provides no further information about their properties. There are some specialized metal detectors that can differentiate between certain metals or respond to only ferrous materials. However to build a such detector much knowledge, skill and experience is needed. The most important characteristic of my circuit is that the presence of a metal close to the search coil triggers a change in the circuit.

This is a vital characteristic of the beat frequency metal detectors. First I will describe what this change is and how it affects the circuit after all. The BFO metal detectors have a resonant frequency, which means the difference between the frequency of the two oscillators, namely oscillator 1 and oscillator 2 whose frequency is fixed. These are two LC oscillators, which have beating frequencies depending on the inductance of the coils and the capacitance of the capacitors in parallel with the inductors.

When these two oscillators are tuned to certain frequencies, usually in the order of 105 Hz, the metal detector mixes, or in other words "e beats" the outputs of the oscillators with each other, creating a so called "beat note" within the audible range (20-20000 Hz). The low pass filter (LPF) and the audio amplifier parts of the metal detector make it possible for us to hear this beat note, the LPF differentiates between sum and difference of the two frequencies and selects the smaller one-the difference, and the amplifier amplifies the magnitude of the resonant sine wave without changing its phase so we can hear the signal. When the search coal interferes with a metal object in proximity, the value of inductance of the search coil changes temporarily, therefore the oscillator that it is a part of then oscillates at a different frequency, changing the resonant frequency as a result. I will explain this phenomenon in more detail as it constitutes the main function of my metal detector (since its BFO type). The frequency of one of the oscillators is adjustable so we can choose the best audio frequency or react to frequency drifts (changes in the beat note due to outside effects such as ground noise, meaning the changes triggered on the circuit by the metals present in the ground) or temperature. Also this adjustment of the beat note is important because the variations in pitch of the note that make it possible for us to detect is more obvious at certain frequencies under certain conditions.

Lastly its needed for the comfort of the listener, because listening to the same frequency for a long time may seriously disturb the users psychological health. In most cases the two oscillators are "ezero beaten" meaning that their output frequencies are approximately equal no beat note is heard under normal conditions. This is also good since small changes usually won't create a note within the audile range (above 20 Hz). However if the detector isn't professionally designed, in this case the oscillators may automatically lock each other so they keep beating at the same frequency no matter what happens.

Also it is hard to fix the circuit in such a case so I won't "ezero beat" my metal detector and choose an appropriate audible beat frequency. Now I will go into theory to describe how these oscillators work on their own. First let me explain what inductance is and how its calculated. If a conductor is wound to form a coil (solenoid of multiple turns) and connected to a power supply, the conductor current will generate its own magnetic field, and the net effect of all these conductor magnetic fields added together to generate a strong magnetic field. This coil of conductor which is used to generate a strong magnetic field is called an electromagnet. A voltage will be induced into this electromagnet when it's subject to a moving magnetic field.

This rule forms the basis of the phenomenon called self-inductance or more commonly called inductance (there is also a type of inductance called mutual-inductance). By definition inductance is the ability of a device to oppose a change in current flow, and the device specifically designed to achieve this function is called an inductor. Here is how inductance is calculated; If a solenoid of length l and cross-sectional area A is wound with N turns of wire, and current I flows through the solenoid. The magnitude of the magnetic field (B) of the solenoid at its center is B = f^EoN I / l, where f^Eo is the permeability of free space equal to 4 f^I x 10-7 T. m. A-1 The magnetic flux ("U) is calculated by the formula "U = BA = f^Einai / l This flux links with each turn; therefore inductance L = N"U / I = f^EoN 2 A / l My search coil has 15 turns, 2.3 x 10-2 m length and 1.00 x 10-2 cross-sectional area. So its inductance is approximately 120 f^EH (the oscilloscope measured it to be 84 f^EH and my reference coil to be 72 f^EH) Now lets see how this opposition occurs in detail.

When a voltage source has been connected across a coil, a current is forced across the coil. This current will rise toward its maximum value, the magnetic field expands, throughout this period of time a relative motion between the magnetic field lines and the conductor will be present. Therefore there will be an induced voltage on the coil. This induced voltage will produce an induced current to oppose the change in the circuit current, the current that produced it, according to Lenz's law. So we can understand that the practical meaning of self-inductance is the induction of back e. m. f in the coil going through a current change. When the current through a coil decreases, again there will be relative motion between the collapsing magnetic field lines and the conductor, inducing a voltage which will create a current in the direction the current was going before.

However after a short period the magnetic field will have totally collapsed, the induced voltage will be zero, and the induced current within the circuit will not be present anymore. All these are results of the law of conservation of energy, here the electrical energy is stored or released in the form of magnetic field energy, just as capacitors store or release electrical energy in the form of electric field. Anyway as I said this induced voltage within the inductor is called counter or back e. m. f. It opposes the applied e. m. f or battery voltage. The ability of a coil or conductor to induce a counter e. m. f within itself as a result of change in current is called self-inductance, or inductance, symbolized as L. The unit of inductance is henry (H). If the inductance of a coil is 1 H, a change in current by 1 A (ampere) per second causes an induced voltage of 1 V. Inductance is therefore a measure of how much counter e. m. f can be generated by an inductor for a given amount of current change through the same inductor.

Now since I have described most of the properties of inductors, I can go on to explain how a piece of metal changes the beat frequency of the metal detector in a little bit more detail. A pulsing current is applied to the search coil, which then induces a magnetic field. When the magnetic field of the coil moves across metal, the field induces electric currents (called eddy currents) in the metal. The eddy currents induce their own magnetic field (if the metal is magnetic, the magnetic field directs into the object, if not out of the object: therefore magnetic objects trigger a decrease in the beat frequency, while others increase it due to the changes of the inductance of the search coil) which generates an opposite current depending on the properties of the search coil and the capacitors in parallel with it, therefore forcing a different output frequency to occur, due to mutual inductance.

In other words, the inductor, the search coil, doesn't anymore function as it did before in the presence of a metal nearby. Therefore since the output of one of the oscillators has changed, the beat note changes in duration and tone as well. After learning the properties of inductors, I wondered how the LC oscillators actually work, meaning how they manage to create resonant frequencies when a dc current is applied to them. Lets consider a resistance less inductor connected between the terminals (legs) of a fixed and charged capacitor. At the instant connections are made, the capacitor starts to discharge through the inductor.

At a later instant, the capacitor has completely discharged and the potential difference between its plates is zero (and through the inductor since they are in parallel). Meanwhile the current in the inductor has created a magnetic field around it. Since the voltage has become zero, and discharging has come to an end, the magnetic field starts to decay. However as I have told according to properties of inductors and Lenz's Law, this decreasing of magnetic field creates an e. m. f which also creates a current same direction as it was before. Therefore the current continues, but decreasing in its magnitude, until the magnetic field has completely disappears and capacitor has been charged opposite to its initial polarity. The process now repeats itself in the reversed direction, and in the absence of energy losses (which never happens in reality) the charges on the capacitor surge back and forth forever.

This process is called electrical oscillation. If we consider the concept of energy in this case, the oscillations of an electrical circuit consist of a transfer of energy back and forth between the forms of electric field energy (capacitors job) and magnetic field energy (inductors job). According to the law of conservation of energy, the total energy circulating in the circuit is must be constant. This is very analogous to the case of transfer of energy in an oscillating mechanical system from kinetic energy to potential energy, just like the situation of a mass on a spring.