Metal Detectors: Difference between revisions

Latest revision as of 02:35, 4 December 2015

Claimed by Kristie Choe

Short Description of Topic

Introduction to the invention of metal detectors and the physics behind the tool.

The Main Idea

Metal detectors are electromagnetic devices using Faraday's Law used to sense the presence of metal within its reach.

How They Work

Simple metal detectors have two types of coils: transmitter coils, coils of wire wrapped around the typically circular head at the end of the device's handle and receiver coils. According to Maxwell's equations, as the electricity flows through the transmitter coil and creates an electric field, so too does a magnetic field occur all around it as well. It is necessary for the user to move the detector across the ground so that the magnetic field will move around too. By moving the detector over a metal object, the moving magnetic field around the detector affects the atoms inside the metal, causing the electrons to move in a different manner. Simply put, the detector's moving magnetic field induces electrical activity in the metal object, in turn, now causing another magnetic field to appear around the metal object.

The metal detector is able to detect this new magnetic field because of the receiver coil that is connected to a circuit with a loudspeaker. When the detector moves around the metal object, the induced magnetic field on the object cuts through the coil, causing electricity to flow through the receiver coil, which makes the loudspeaker beep or click. The closer the transmitter coil is to the object, the louder the noise will be from the receiver coil.

A Mathematical Model

Faraday's Law, which states [math]\displaystyle{ \mathcal{E} = -{{d\Phi_B} \over dt} \ }[/math], where [math]\displaystyle{ \mathcal{E} }[/math] is the emf produced from the time-varying magnetic flux Φ_B. The flux is given by [math]\displaystyle{ \int_{\Sigma} \mathbf{B} \cdot d\mathbf{A}. }[/math]

The figure below shows a sketch of the effect of a metal object on the magnetic flux when placed in the vicinity of the receiver coil.

Applications of Faraday's Law and Biot-Savart Law in finding magnetic flux and emf:

Emf induced in the pick-up coil: [math]\displaystyle{ \mathcal{E} = -N_p{{d\Phi} \over dt} \ }[/math]

[math]\displaystyle{ \mathcal{\Phi} }[/math] is the magnetic flux in the receiver coil due to the magnetic field produced by the transmitter coil

[math]\displaystyle{ N_p }[/math] is the number of turns in the receiver coil

Biot-Savart Law gives magnitude of the magnetic field at the center:

[math]\displaystyle{ B = N_f{\mu_0}I(t)/(2R_f) }[/math]

[math]\displaystyle{ {{\mu_0}}= 4{\pi}{E-7} }[/math] is the vacuum permeability constant

[math]\displaystyle{ N_p }[/math] is the number of turns in transmitter coil

[math]\displaystyle{ R_f }[/math] is the radius of the transmitter coil

Approximate magnetic flux of the receiver coil:

[math]\displaystyle{ \mathcal{\Phi} = ({\pi}R_p^2)N_f{{\mu_0}}I(t)/(2R_f) }[/math]

Emf induced in receiver coil:

[math]\displaystyle{ \mathcal{E} = {{\mu_0}}N_pN_f{\pi}R_P^2/(2R_f) {dI(t) \over dt} \ }[/math]

A Visual Model

1. The transmitter coil (red circle) is connected to a circuit (red).

2. The transmitter coil induces a magnetic field around it.

3. When the detector moves across a metal object (3), the magnetic field cuts through it.

4. The magnetic field induces an electrical current flow inside the metal object (yellow).

5. This electric field creates a second magnetic field around the metal object (blue arrows), which cuts through the receiver coil (blue circle). This, in turn, causes an electric current to flow through the receiver coil and into the circuit (blue) at the top, making a noise.

Examples of metal detector models

Connectedness

This is a topic that I am interested in because I have always wanted to own a metal detector. It is eye-opening to see how the physics I have been learning this semester relates to this device when I never thought twice about how it works. Metal detectors have many applications other than just as metal detectors to look for valuable items, but they can also be used for things such as security purposes to screen for dangerous weapons and the like.

History

The metal detector was invented out of necessity. On July 2, 1881, President James Garfield was shot in Washington, D.C. by a man named Charles J. Guiteau. The President was shot in the back but it was not life-threatening, but the bullet could not be found and it was causing the President to suffer. When Alexander Graham Bell visited the President during this time, he built a metal detector to be able to find this bullet. Unfortunately, the device was unsuccessful due to metal springs in the President's bed that were confusing the device unbeknownst to Bell. President Garfield died of the wound infection on September 19, 1881.

Bell's invention was a prototype to later inventions used to find and clear landmines and unexploded bombs across Europe after both world wars. Then Gerhard Fisher created the first portable metal detector in 1925, but Charles Garrett, an electrical engineer, started metal detecting as a hobby, also reinventing metal detector design at the time.

References

http://www.explainthatstuff.com/metaldetectors.html

http://inside.mines.edu/~jamcneil/TPT_MetalDetector.pdf

http://www.metaldetector.com/learn/metal-detector-history/history-of-the-metal-detector

@@ Line 1: / Line 1: @@
+Claimed by Kristie Choe
 '''Short Description of Topic'''
@@ Line 13: / Line 15: @@
 The metal detector is able to detect this new magnetic field because of the receiver coil that is connected to a circuit with a loudspeaker. When the detector moves around the metal object, the induced magnetic field on the object cuts through the coil, causing electricity to flow through the receiver coil, which makes the loudspeaker beep or click. The closer the transmitter coil is to the object, the louder the noise will be from the receiver coil.
+===A Mathematical Model===
+Faraday's Law, which states <math>\mathcal{E} = -{{d\Phi_B} \over dt} \ </math>,  where <math>\mathcal{E}</math> is the emf produced from the time-varying magnetic flux Φ<sub>''B''</sub>. The flux is given by <math> \int_{\Sigma} \mathbf{B} \cdot d\mathbf{A}. </math>
-===A Mathematical Model===
+The figure below shows a sketch of the effect of a metal object on the magnetic flux when placed in the vicinity of the receiver coil.
+[[File:Textbook.png]]
+Applications of Faraday's Law and Biot-Savart Law in finding magnetic flux and emf:
+Emf induced in the pick-up coil:
+<math>\mathcal{E} = -N_p{{d\Phi} \over dt} \ </math>
+<math>\mathcal{\Phi}</math> is the magnetic flux in the receiver coil due to the magnetic field produced by the transmitter coil
+<math>N_p</math> is the number of turns in the receiver coil
+Biot-Savart Law gives magnitude of the magnetic field at the center:
+<math>B = N_f{\mu_0}I(t)/(2R_f)</math>
+<math>{{\mu_0}}= 4{\pi}{E-7}</math> is the vacuum permeability constant
+<math>N_p</math> is the number of turns in transmitter coil
+<math>R_f</math> is the radius of the transmitter coil
+Approximate magnetic flux of the receiver coil:
+<math>\mathcal{\Phi} = ({\pi}R_p^2)N_f{{\mu_0}}I(t)/(2R_f)</math>
+Emf induced in receiver coil:
-The primary physics equation used when analyzing spark plugs is Faraday's Law, which states <math>\mathcal{E} = -{{d\Phi_B} \over dt} \ </math>,  where <math>\mathcal{E}</math> is the emf produced from the time-varying magnetic flux Φ<sub>''B''</sub>. The flux is given by <math> \int_{\Sigma} \mathbf{B} \cdot d\mathbf{A}. </math>
+<math>\mathcal{E} = {{\mu_0}}N_pN_f{\pi}R_P^2/(2R_f) {dI(t) \over dt} \ </math>
-The spark plug essentially consists of 2 coils, a primary coil and a much larger secondary coil. As current from the car battery runs through the primary coil, it is interrupted by cam action, which varies the electric current running through the circuit. Because the primary coil is is wrapped around the secondary coil, a varying magnetic field induces an electric current to be run through the secondary coil, which is much larger, which in turn produces a much larger EMF due to the number of loops in the coil.
+===A Visual Model===
-<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
+. The transmitter coil (red circle) is connected to a circuit (red).
-===A Computational Model===
+. The transmitter coil induces a magnetic field around it.
-How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
+. When the detector moves across a metal object (3), the magnetic field cuts through it.
-==Examples==
+. The magnetic field induces an electrical current flow inside the metal object (yellow).
-[[File:Spark Plug(1).jpg]]
+. This electric field creates a second magnetic field around the metal object (blue arrows), which cuts through the receiver coil (blue circle). This, in turn, causes an electric current to flow through the receiver coil and into the circuit (blue) at the top, making a noise.
-Anatomy of a Typical Spark Plug
+[[File:visual123.png]] [[File:visual4.png]] [[File:visual5.png]]
-[[File:firing spark plug.jpg]]
+==Examples of metal detector models==
-===Simple===
+[[File:Simpledetector.png]]  [[File:newdetector.jpg]]
-===Middling===
-===Difficult===
 ==Connectedness==
-#How is this topic connected to something that you are interested in?
-#How is it connected to your major?
+This is a topic that I am interested in because I have always wanted to own a metal detector. It is eye-opening to see how the physics I have been learning this semester relates to this device when I never thought twice about how it works. Metal detectors have many applications other than just as metal detectors to look for valuable items, but they can also be used for things such as security purposes to screen for dangerous weapons and the like.
-#Is there an interesting industrial application?
 ==History==
-Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
+The metal detector was invented out of necessity. On July 2, 1881, President James Garfield was shot in Washington, D.C. by a man named Charles J. Guiteau. The President was shot in the back but it was not life-threatening, but the bullet could not be found and it was causing the President to suffer. When Alexander Graham Bell visited the President during this time, he built a metal detector to be able to find this bullet. Unfortunately, the device was unsuccessful due to metal springs in the President's bed that were confusing the device unbeknownst to Bell. President Garfield died of the wound infection on September 19, 1881.
+Bell's invention was a prototype to later inventions used to find and clear landmines and unexploded bombs across Europe after both world wars. Then Gerhard Fisher created the first portable metal detector in 1925, but Charles Garrett, an electrical engineer, started metal detecting as a hobby, also reinventing metal detector design at the time.
 == See also ==
-[http://www.physicsbook.gatech.edu/Magnetic_Field_of_a_Solenoid Magnetic Field of a Solenoid]
+[http://www.physicsbook.gatech.edu/Biot-Savart_Law Biot-Savart Law]
-[http://www.physicsbook.gatech.edu/Curly_Electric_Fields Curly Electric Fields]
+[http://www.physicsbook.gatech.edu/Magnetic_Force Magnetic Force]
 [http://www.physicsbook.gatech.edu/Faraday%27s_Law Faraday's Law]
@@ Line 57: / Line 88: @@
 [http://www.physicsbook.gatech.edu/Inductance Inductance]
-[http://www.physicsbook.gatech.edu/Transformers_from_a_physics_standpoint Transformers]
+==References==
-===Further reading===
-Books, Articles or other print media on this topic
-===External links===
-[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]
+[http://www.explainthatstuff.com/metaldetectors.html/ http://www.explainthatstuff.com/metaldetectors.html]
-==References==
+[http://inside.mines.edu/~jamcneil/TPT_MetalDetector.pdf/ http://inside.mines.edu/~jamcneil/TPT_MetalDetector.pdf]
-This section contains the the references you used while writing this page
-[[Category:Which Category did you place this in?]]
+[http://www.metaldetector.com/learn/metal-detector-history/history-of-the-metal-detector/ http://www.metaldetector.com/learn/metal-detector-history/history-of-the-metal-detector]