Magnetic Torque: Difference between revisions
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===Units Discussion=== | ===Units Discussion=== | ||
''' | '''τ''' has units of N*m | ||
''' | |||
'''µ''' has units of A*m^^2 | |||
'''B''' has units of tesla | '''B''' has units of tesla | ||
From this, it must be that one N*m(which interestingly defines work) is equal to one tesla * A*m^^2. | From this, it must be that one N*m(which interestingly defines work) is equal to one tesla * A*m^^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example. | ||
[[File:torque.jpg]] This is the overall equation for determining magnetic torque. | "[[File:torque.jpg]] This is the overall equation for determining magnetic torque. | ||
[[File:theT.jpg]] Represents torque (in units of N*m) | [[File:theT.jpg]] Represents torque (in units of N*m) | ||
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[[File:mu.jpg]] is the dipole moment of the magnet (A*m^^2) | [[File:mu.jpg]] is the dipole moment of the magnet (A*m^^2) | ||
[[File:theB.jpg]] is the magnetic field created by the magnet (in units of Tesla) | [[File:theB.jpg]] is the magnetic field created by the magnet (in units of Tesla)" - planned to be edited out of the wiki page | ||
===A Computational Model=== | ===A Computational Model=== |
Revision as of 17:04, 27 November 2016
Claimed by Demetria Hubbard--Dhubbard8 (talk) 15:02, 2 December 2015 (EST) edited by Hannah Jang Spring 2016. Claimed by Timmy Donohue Fall 2016 (Edits to include explanation to examples, improved mathematical model, improved history, improved connectedness, added external links, units explanation)
Magnetic torque is a phenomenon that occurs when the magnetic field produced causes a current-carrying wire to twist out of proportion.
The Main Idea
The idea behind this concept is that as current flows through a wire, a magnetic field is produced. While this magnetic field is being produced, there is a force acting upon the wire causing it to twist. An example of this phenomenon is the movement of a compass needle by the Earth's magnetic field. Another example is a hanging coil that twists in the direction of the magnetic field of a bar magnet.
The magnetic torque acts on the dipole, and it is highly dependent on the magnetic moment and external magnetic field.
Several factors besides the magnetic moment and external magnetic field can affect the magnetic torque. In a loop or other three dimensional object the orientation of the object relative to the magnetic field highly affects the torque.
This relationship can be seen in this video: [1]
Here is a video on Asymmetric Magnet Torque Asymmetric Magnet Torque
A Mathematical Model
The overarching equation that encapsulates this physical phenomena is as follows:
- [math]\displaystyle{ \boldsymbol{\tau} = \boldsymbol{\mu} \times\mathbf{B} }[/math]
where:
τ is the variable describing torque
μ is the magnetic dipole
B is the magnetic field
Units Discussion
τ has units of N*m
µ has units of A*m^^2
B has units of tesla
From this, it must be that one N*m(which interestingly defines work) is equal to one tesla * A*m^^2. From a discussion of units alone, it is important to think about what sorts of questions the professor might ask, meaning questions could include an analyses of the work that must be added to a system to keep it stationary for example.
" This is the overall equation for determining magnetic torque.
Represents torque (in units of N*m)
is the dipole moment of the magnet (A*m^^2)
is the magnetic field created by the magnet (in units of Tesla)" - planned to be edited out of the wiki page
A Computational Model
Click here to view the PHET Interactive Model created by the University of Colorado
PHET Interactive Magnet and Compass Model
Examples
Torque on Current Carrying Loop
Simple
A bar magnet whose magnetic dipole moment is <3, 0, 1.8> A · m2 is suspended from a thread in a region where external coils apply a magnetic field of <0.6, 0, 0> T. What is the vector torque that acts on the bar magnet?
Middling
A bar magnet whose magnetic dipole moment is 14 A · m2 is aligned with an applied magnetic field of 5.4 T. How much work must you do to rotate the bar magnet 180° to point in the direction opposite to the magnetic field?
Difficult
A cylindrical bar magnet whose mass is 0.09 kg, diameter is 1 cm, length is 3 cm, and whose magnetic dipole moment is <4, 0, 0> A · m2 is suspended on a low-friction pivot in a region where external coils apply a magnetic field of <2.0, 0, 0> T. You rotate the bar magnet slightly in the horizontal plane and release it. (For small angles in radians, assume sin(θ) ≈ θ.)
(a) What is the angular frequency of the oscillating magnet?
(b) What would be the angular frequency if the applied magnetic field were <4.0, 0, 0> T?
A detailed description and symbolic representation of magnetic torque can be seen here: Magnetic Torque and Magnetic Dipole Moment
Connectedness
Utilizing a compass is a basic survival need and it just so happens to depend on the torque produced by the Earth's magnetic field. As a Biology major, field work is a large part of what I do, especially studying ecological systems and different habitats. In order to navigate in unfamiliar locations, such as deserts and dense tropical forests, scientists rely heavily on basic survival skills and this includes the use of compasses and maps. Physics, biology, and chemistry make up part of the science family and each heavily depends on the other, this is why it is important to study each one to bridge the relationship.
First paragraph of "Connectedness" written by Demetria Hubbard 2015
The Earth has a complex magnetic field and magnetic dipole moment that creates a magnetic torque. The necessity of all three of these magnetic properties is rarely known; however, all three are essential for life on earth. Earth's magnetic field serves to deflect most of the solar wind, so without the magnetic properties of the earth, the charged solar wind would have stripped the ozone layer from earth which would have exposed everything on earth to dangerous UV radiation.
History
Refer to Magnetic Force
The great importance of magnetic torque that is used in compasses cannot be ignored. The history of the compass and earth's magnetic field are very valuable. The tendency of a magnet to align itself was discovered by the Chinese about 2000 years ago. The magnetic compass became a valuable commodity to European navigators in the 12th century, and in 1600, William Gilbert published De Magnete, which concluded that the earth behaves as a giant magnet. Several theories since then have been made to explain how a magnetic field is produced by the earth. The most accepted theory is that the energy from the radioactivity of the earth's core travels outwards as heat. This heat produces a thermal convection core that creates the earth's magnetic field.
See also
Further reading
- Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 3rd ed. Hoboken, NJ: Wiley, 2011. Print.
- Eisberg, R. and Resnick, R. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. New York: Wiley, p. 269, 1985.
- Griffiths, D. J. Introduction to Electrodynamics, 3rd ed. Englewood Cliffs, NJ: Prentice Hall, p. 220, 1989.
External links
References
- Torque Example
- Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 3rd ed. Hoboken, NJ: Wiley, 2011. Print.
- "Magnet and Compass PHET Interaction Model." PhET. Ed. Chris Malley. University of Colorado, 2015. Web. 5 Dec. 2015. <https://phet.colorado.edu/en/simulation/legacy/magnet-and-compass>.
- Torque on Current-Carrying Loop in Magnetic Field. Doc Schuster. 23 Jan. 2013. Video. https://www.youtube.com/watch?v=xER1_SYql44
- http://helenotway.edublogs.org/2011/01/02/different-compass-point-same-ultimate-direction/
- Weisstein, Eric. "Magnetic Torque." Eric Weisstein's World of Physics. Wolfram Research, 1996. Web. 5 Dec. 2015. <http://scienceworld.wolfram.com/physics/MagneticTorque.html>.
- "Magnetic Torques and Amp's Law." Rochester Institute of Technology. Web. 5 Dec. 2015. <http://spiff.rit.edu/classes/phys213/lectures/amp/amp_long.html>.
- "Homework 11." WebAssign. Web. 5 Dec. 2015. <http://webassign.net/>.
- Magnetic Torque. Animations for Physics and Astronomy. 15 Feb. 2008. Video. https://www.youtube.com/watch?v=xER1_SYql44
- Digital image. N.p., n.d. Web. 17 Apr. 2016.
- "Discovery of the Earth’s Magnetic Field." GNS Science. N.p., n.d. Web. 17 Apr. 2016. <http://www.gns.cri.nz/Home/Our-Science/Earth-Science/Earth-s-Magnetic-Field/Discovery-of-the-Earth-s-magnetic-field>.
- "Magnetic Dipole Moment." Hyperphysics, n.d. Web. 17 Apr. 2016. <http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html>.
- Magnetic Torque and Magnetic Dipole Moment. AK Lectures. 7 Dec. 2013. Video. https://www.youtube.com/watch?v=K1FEepXKETM