Magnetic Torque: Difference between revisions

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Essentially, there are only a few categories of questions that can be asked relating to magnetic torque.  These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location.  In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: '''|τ| = µ*Bcos|90|= µ*B'''.  This is the essential question involving the equation listed above for magnetic torque.  However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.  The relationship is defined in the following illustration
Essentially, there are only a few categories of questions that can be asked relating to magnetic torque.  These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location.  In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: '''|τ| = µ*Bcos|90|= µ*B'''.  This is the essential question involving the equation listed above for magnetic torque.  However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum.  The relationship is defined in the following illustration


[[File:Wiki Explanation.jpg]]
[[File:Wiki Explanation]]


[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]
[https://www.youtube.com/watch?v=xER1_SYql44 Torque on Current Carrying Loop]

Revision as of 17:12, 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.

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Example of Magnetic Torque


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 and can be found using many expressions including that of a wire which relates magnetic dipole to the current in the wire multiplied by its cross sectional area. For a magnet, this quanity is not easily derived, and is a little outside the scope of this discussion. This quanitity is usually given in the problem statement. However, for a video that helps describe the magnetic dipole moment of a magnet: [2]

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.

A Computational Model

Click here to view the PHET Interactive Model created by the University of Colorado

PHET Interactive Magnet and Compass Model

Examples

Essentially, there are only a few categories of questions that can be asked relating to magnetic torque. These questions include a simple computation of magnetic torque given the dipole moment of a magnet, and the magnetic field being applied to the observation location. In this situation, you can either utilize a simple cross product, as in the equation listed above, or if the values are given as scalars, and it is known that they are perpendicular to each other in direction, you can utilize the equation: |τ| = µ*Bcos|90|= µ*B. This is the essential question involving the equation listed above for magnetic torque. However, the professor can also ask questions relating to material learned from physics 1 involving angular frequencies and other products of angular momentum. The relationship is defined in the following illustration

File:Wiki Explanation

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

A standard compass http://helenotway.edublogs.org/2011/01/02/different-compass-point-same-ultimate-direction/

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.

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The orientations of compasses at different points in the Earth's magnetic field/

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

Magnetic Torque

References

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