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Found an error in the circular orbit equation. Checking n dot p a second time to determine if the orbit should be 'theta' or '2pi - theta' is invalid, since that is already what is used in the arccos. n dot v is the correct approach.
 
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'''Specific absorption rate''' (SAR) is a measure of the rate at which [[energy]] is [[Absorption (electromagnetic radiation)|absorbed]] by the human body when exposed to a [[radio frequency]] (RF) [[electromagnetic field]]; although, it can also refer to absorption of other forms of energy by tissue, including [[ultrasound]].<ref>{{cite journal|author=Sun J, Hynynen K |url=http://www.ncbi.nlm.nih.gov/pubmed/9745750 |title=Focusing of therapeutic ultrasound through a human skull: a numerical study |journal=[[J Acoust Soc Am]] |date=September 1998 |pmid=9745750 |date=2013-08-12 |accessdate=2013-12-12| bibcode=1998ASAJ..104.1705S| volume=104| pages=1705–15| doi=10.1121/1.424383|issue=3 Pt 1}}</ref> It is defined as the [[Power (physics)|power]] absorbed per [[mass]] of [[body tissue|tissue]] and has units of [[watt]]s per [[kilogram]] (W/kg).<ref>{{cite book | author= Jianming Jin | title= Electromagnetic Analysis and Design in Magnetic Resonance Imaging | year= 1998 | publisher= CRC Press | isbn= 978-0-8493-9693-9 | pages = §5.3.3 pp. 226ff }}</ref>
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SAR is usually averaged either over the whole body, or over a small sample volume (typically 1&nbsp;g or 10&nbsp;g of tissue). The value cited is then the maximum level measured in the body part studied over the stated volume or mass.
 
== Calculation ==
 
SAR for electromagnetic energy can be calculated from the [[electric field]] within the tissue as:
 
:<math>\text{SAR} = \int_\textrm{sample} \frac{\sigma(\mathbf{r}) |\mathbf{E}(\mathbf{r})|^2}{\rho(\mathbf{r})} d\mathbf{r}</math>
 
where
:<math>\sigma</math> is the sample [[electrical conductivity]]
:<math>E</math> is the [[Root mean square|RMS]] electric field
:<math>\rho</math> is the sample [[density]]
 
SAR measures exposure to fields between 100&nbsp;kHz and 10&nbsp;GHz (generally known as radio waves).<ref name=icnirp>{{cite web|url=http://www.icnirp.org/documents/emfgdl.pdf|title=ICNIRP Guidelines For Limiting Exposure To The Time-Varying Electric, Magnetic And Electromagnetic Fields (Up To 300 GHz)|publisher=[[International Commission on Non-Ionizing Radiation Protection]]|year=1998|accessdate=2013-12-12}}</ref> It is commonly used to measure power absorbed from [[mobile phones]] and during [[MRI]] scans. The value will depend heavily on the geometry of the part of the body that is exposed to the RF energy, and on the exact location and geometry of the RF source. Thus tests must be made with each specific source, such as a mobile phone model, and at the intended position of use.
 
=== Mobile phone SAR testing ===
{{see also|Mobile phone radiation and health|Comparison of specific absorption rate for devices#Smartphones}}
When measuring the SAR due to a mobile phone the phone is placed at the head in a talk position. The SAR value is then measured at the location that has the highest absorption rate in the entire head, which in the case of a mobile phone is often as close to the phone's antenna as possible. Various governments have defined maximum SAR levels for RF energy emitted by mobile devices:
 
*[[United States]]: the [[Federal Communications Commission|FCC]] requires that phones sold have a SAR level at or below 1.6&nbsp;[[watt]]s per [[kilogram]] (W/kg) taken over the volume containing a mass of 1&nbsp;gram of tissue that is absorbing the most signal.
*[[European Union]]: [[CENELEC]] specify SAR limits within the EU, following [[International Electrotechnical Commission|IEC]] standards. For mobile phones, and other such hand-held devices, the SAR limit is 2&nbsp;W/kg averaged over the 10&nbsp;g of tissue absorbing the most signal ([http://webstore.iec.ch/webstore/webstore.nsf/artnum/033746 IEC 62209-1]).
*[[India]]: switched from the EU limits to the US limits for mobile handsets in 2012. Unlike the US, India will not rely solely on SAR measurements provided by manufacturers; random compliance tests are done by a government-run [[Telecom Engineering Centre]] (TEC) SAR Laboratory on handsets and 10% of towers. All handsets must have a hand free mode.<ref name=IAreg>{{cite web|url=http://www.pib.nic.in/newsite/erelease.aspx?relid=87152 |title=Stringent Mobile Radiation Standards Come into Force from tomorrow New Mobile Handsets to comply with SAR Value of 1.6W/KG - Penalty, Random Checks Introduced for Enforcement |publisher=[[Press Information Bureau]], Government of India |date=2012-08-31 |accessdate=2013-12-22}}</ref>
 
SAR values are heavily dependent on the size of the averaging volume. Without information about the averaging volume used, comparisons between different measurements cannot be made. Thus, the European 10-gram ratings should be compared among themselves, and the American 1-gram ratings should only be compared among themselves.
 
=== MRI scanner SAR testing ===
For Magnetic Resonance Imaging the limits (described in [http://webstore.iec.ch/Webstore/webstore.nsf/artnum/043851?opendocument IEC 60601-2-33]) are slightly more complicated:
 
{| class="wikitable" style="text-align: center;"
|-
|
! Whole body SAR
! Partial body SAR
! Head SAR
! colspan="3" | Local SAR (a)
|-
! Body Region →
| whole body
| exposed body part
| head
| head
| trunk
| extremities
|-
! Operating Mode ↓
| (W/kg)
| (W/kg)
| (W/kg)
| (W/kg)
| (W/kg)
| (W/kg)
|-
! Normal
| 2
| 2 - 10 (b)
| 3.2
| 10 (c)
| 10
| 20
|-
! 1st Level Controlled
| 4
| 4 - 10 (b)
| 3.2
| 20 (c)
| 20
| 40
|-
! 2nd Level Controlled
| &gt;4
| &gt;(4 - 10) (b)
| &gt;3.2
| &gt;20 (c)
| &gt;20
| &gt;40
|-
! Short duration SAR
| colspan="6" | The SAR limit over any 10 s period shall not exceed two times the stated values
|}
:'''Note''': Averaging time of 6 minutes.
(a) Local SAR is determined over the mass of 10&nbsp;g.
 
(b) The limit scales dynamically with the ratio "exposed patient mass / patient mass":
 
NORMAL OPERATING MODE: Partial body SAR = 10&nbsp;W/kg – (8&nbsp;W/kg * exposed patient mass / patient mass)<br>
FIRST LEVEL CONTROLLED OPERATING MODE: Partial body SAR = 10&nbsp;W/kg – (6&nbsp;W/kg * exposed patient mass / patient mass)
 
(c) In cases where the orbit is in the field of a small local RF transmit coil, care should be taken to ensure that the temperature rise is limited to 1&nbsp;°C.
 
==Criticism==
 
SAR limits set by law don't consider that the human body is particularly sensitive to the power peaks or frequencies responsible for the [[microwave hearing effect]].<ref name="frey2">{{cite journal| url=http://jap.physiology.org/content/17/4/689.abstract?sid=7c073ad2-6324-4b47-94e1-124dc0a5f154 | journal=Journal of Applied Physiology| volume=17 |pages=689–692 |year=1962| title=Human auditory system response to modulated electromagnetic energy |author=Allan H. Frey |accessdate=| pmid=13895081}}</ref><ref name="frey-headaches">{{cite journal|author=Frey, A.H.  |title=Headaches from cellular telephones: are they real and what are the implications? |year=1998 |volume=106 |publisher=[[National Institute of Environmental Health Sciences]] |date=2013-08-12 |journal=[[Environmental Health Perspectives]] |pmc=1533043 |issue=3|doi=10.1289/ehp.98106101|pages=101–103}}</ref> Frey reports that the microwave hearing effect occurs with average power density exposures of 400 μw/cm<sup>2</sup>, well below SAR limits (as set by government regulations).<ref name="frey2" />
 
Notes:
 
In comparison to the short term, relatively intensive exposures described above, for long term environmental exposure of the general public there is a limit of 0.08&nbsp;W/kg averaged over the whole body.<ref name=icnirp/> A whole-body average SAR of 0.4&nbsp;W/kg has therefore been chosen as the restriction that provides adequate protection for occupational exposure. An additional safety factor of 5 is introduced for exposure of the public, giving an average whole-body SAR limit of 0.08&nbsp;W/kg.
 
===FCC advice===
The FCC Guide, "Specific Absorption Rate (SAR) For Cell Phones: What It Means For You," after detailing the limitations of SAR values, offers the following "bottom line" editorial:
 
{{quote|"ALL cell phones must meet the FCC’s RF exposure standard, which is set at a level well below that at which laboratory testing indicates, and medical and biological experts generally agree, adverse health effects could occur. For users who are concerned with the adequacy of this standard or who otherwise wish to further reduce their exposure, the most effective means to reduce exposure are to hold the cell phone away from the head or body and to use a speakerphone or hands-free accessory. These measures will generally have much more impact on RF energy absorption than the small difference in SAR between individual cell phones, which, in any event, is an unreliable comparison of RF exposure to consumers, given the variables of individual use." <ref>{{cite web|url=http://www.fcc.gov/guides/specific-absorption-rate-sar-cell-phones-what-it-means-you |title=Specific Absorption Rate (SAR) For Cell Phones: What It Means For You |publisher=[[Federal Communications Commission]] |date= |accessdate=2013-12-22}}</ref>}}
<!-- Alternate quote format
{{quote box
|width= 100%
|salign= right
|quote= <big>"ALL cell phones must meet the FCC’s RF exposure standard, which is set at a level well below that at which laboratory testing indicates, and medical and biological experts generally agree, adverse health effects could occur. For users who are concerned with the adequacy of this standard or who otherwise wish to further reduce their exposure, the most effective means to reduce exposure are to hold the cell phone away from the head or body and to use a speakerphone or hands-free accessory. These measures will generally have much more impact on RF energy absorption than the small difference in SAR between individual cell phones, which, in any event, is an unreliable comparison of RF exposure to consumers, given the variables of individual use."</big>
|source= — FCC guide: "Specific Absorption Rate (SAR) For Cell Phones: What It Means For You"<ref>{{cite web|url=http://www.fcc.gov/guides/specific-absorption-rate-sar-cell-phones-what-it-means-you |title=Specific Absorption Rate (SAR) For Cell Phones: What It Means For You |publisher=[[Federal Communications Commission]]|date= |accessdate=2013-12-22}}</ref>
}}
-->
 
==See also==
*[[Comparison of specific absorption rate for devices]]
*[[Dielectric heating]]
*[[Electromagnetic radiation and health]]
 
==References==
{{Reflist|30em}}
 
==External links==
*[http://www.antenna-theory.com/tutorial/cancer/cellphone.php#sar Radiation in Mobile Phones: An Analysis] antenna-theory.com
*[http://www.fcc.gov/cgb/sar/ FCC: Cellular Telephone Specific Absorption Rate]
*[http://www.who.int/mediacentre/factsheets/fs193/en/ World Health Organization: Electromagnetic fields and public health]
*[http://reviews.cnet.com/4520-6602_7-5020355-1.html?tag=nl.e404/ Cell Phone Radiation Levels, CNET article and comprehensive listings]
*[http://www.ets-lindgren.com/pdf/sar_lo.pdf An Update on SAR Standards and the Basic Requirements for SAR Assessment]
*[http://rfhealth-sar.motorola.com/SAR/sar.html Motorola's SAR Website]
*[http://sar.nokia.com/sar/index.jsp Nokia's SAR Website]
*[http://www.samsung.com/sar/sarMain?site_cd=in&prd_mdl_name=S3500&selNatCd=GB&languageCode=EN Samsung mobile's SAR website]
*[http://www.sonyericsson.com/health Sony Ericsson's SAR Website]
*[http://www.sarshield.com/english/radiationchart.htm SAR of some mobile phones]
*[https://apps.fcc.gov/eas/GetApplicationAttachment.html?id=1336224 Example of a detailed SAR report on the FCC web site (for an Apple iPod Touch 4G)]
 
[[Category:Radiobiology]]
[[Category:Biophysics]]

Latest revision as of 10:21, 7 November 2014

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