Encyclopedia Magnetica™

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
=== Calculator of H along axis of rectangular magnet ===

<box 100% #efffef>
|< 100% 10% 90% >|
|  {{/calculator/icon_calc.png?60&nolink}}  | //[[user/Stan Zurek]], Calculator of H along axis of rectangular magnet, Encyclopedia Magnetica//, \\ @PAGEL@, {accessed: @YEAR@-@MONTH@-@DAY@} |
</box>

^  [[/Magnetic field strength]] //H// of a cuboid (rectangular) [[/permanent magnet]] along its axis   ^^
| //Source [1] [[https://isbnsearch.org/isbn/0122699513|Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513]]//  ||
| //[1], eq. (3.114), p. 135 (converted by [[/user/Stan Zurek]] to be expressed by [[/remanence flux density]] rather than [[/saturation magnetisation]] //   ||
| $$ H(x) = \frac{B_r}{π·µ_0}· \left(  \text{atan} \frac{2·(x+L)·\sqrt{a^2+b^2+4·(x+L)^2}}{a·b} - \text{atan} \frac{2·x·\sqrt{a^2+b^2+4·x^2}}{a·b} \right) $$ |  (A/m)  |
| where: $B_r$ - [[/remanence]] ([[/flux density]]) of the [[/permanent magnet]] (T), $L$ - axial length of the cuboid magnet (m), $a$ and $b$ - lengths (m) of the sides of the cuboid magnet, $x$ - location (m) from the surface of the magnet (surface is synonymous with //x// = 0), //μ//<sub>0</sub> - [[/magnetic permeability of vacuum]] (H/m)  ||

<box 40% right #f0f0f0>
Magnetic field along the axis of a cuboid [[/magnet]] 
[[file/rectangular_magnet_field_magnetica_png|{{/rectangular_magnet_field_magnetica.png}}]]
{{page>insert/by_SZ}}
</box>

<HTML>
<!-- ==================== calculator starts here ============== -->
<HEAD>
<SCRIPT Language="JavaScript">

<!--
/**
 * Function that introduces calculator of a given function.
 **/
 
function getSelectedValue3(selectList){
   return selectList[selectList.selectedIndex].value
}

function calculate_function3(frm){
// set up variables
var Br       = frm.Br.value
var a        = frm.a.value
var b        = frm.b.value
var Lr       = frm.Lr.value
var xr       = frm.xr.value
//var part1r = 0
//var part2r = 0

var a_unit      = getSelectedValue3(frm.a_unit)
var b_unit      = getSelectedValue3(frm.b_unit)
var Lr_unit     = getSelectedValue3(frm.Lr_unit)
var xr_unit     = getSelectedValue3(frm.xr_unit)
var hr_unit     = getSelectedValue3(frm.hr_unit)
var br_unit     = getSelectedValue3(frm.br_unit)
const pi = 3.1415926535897932384626433832795
const u0 = pi*4e-7


// read values and convert to numbers
Br   = parseFloat(Br) 
a    = parseFloat(a) * a_unit
b    = parseFloat(b) * b_unit
Lr   = parseFloat(Lr) * Lr_unit 
xr   = parseFloat(xr) * xr_unit

// calculate the main function

part1r = Math.atan(  (  2*(xr+Lr) * Math.sqrt(  4*(xr+Lr)*(xr+Lr) + a*a + b*b)   )/(a*b)     )

part2r = Math.atan(  (     2 * xr * Math.sqrt(  4*(xr*xr) + a*a + b*b)   )/(a*b)     )

result_rect_b = (Br / pi ) * ( part1r - part2r) * br_unit

result_rect_h = result_rect_b * hr_unit / br_unit / u0

// format number to x digits precision, otherwise result will equal 5.611e+2
result_rect_b = result_rect_b.toPrecision(6)
result_rect_h = result_rect_h.toPrecision(6)

// display result
frm.result_rect_b.value = result_rect_b
frm.result_rect_h.value = result_rect_h

}

//-->
</SCRIPT>
</HEAD>
<body>

<form method="post" action="">
 
Remanence <b><i>B<sub>r</sub></i></b> = <input type="text" value="1" name="Br" size="7" maxlength="10" onChange="calculate_function3(this.form)"> (T)
        
&nbsp;&nbsp;&nbsp;&nbsp;

<br><br>

Side <b><i>a</i></b> = <input type="text" value="30" name="a" size="7" maxlength="10" onChange="calculate_function3(this.form)"> 

           <SELECT name="a_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1e-3" selected>(mm)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="2.54e-2">(inch)</OPTION>
           <OPTION value="1">(m)</OPTION>
        </SELECT>
        
&nbsp;&nbsp;&nbsp;&nbsp;

<br><br>

Side <b><i>b</i></b> = <input type="text" value="20" name="b" size="7" maxlength="10" onChange="calculate_function3(this.form)"> 

           <SELECT name="b_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1e-3" selected>(mm)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="2.54e-2">(inch)</OPTION>
           <OPTION value="1">(m)</OPTION>
        </SELECT>
        
<br><br>

Length <b><i>L</i></b> = <input type="text" value="10" name="Lr" size="7" maxlength="10" onChange="calculate_function3(this.form)"> 

           <SELECT name="Lr_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1e-3" selected>(mm)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="2.54e-2">(inch)</OPTION>
           <OPTION value="1">(m)</OPTION>
        </SELECT>
        
&nbsp;&nbsp;&nbsp;&nbsp;    


<br><br>

Position on axis <b><i>x</i></b> = <input type="text" value="0" name="xr" size="7" maxlength="10" onChange="calculate_function3(this.form)"> 

           <SELECT name="xr_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1e-3" selected>(mm)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="2.54e-2">(inch)</OPTION>
           <OPTION value="1">(m)</OPTION>
        </SELECT><br><br>

        <input type="button" name="Button" value="== Calculate ==" onClick="calculate_function3(this.form)">

<br><br>

<b><i>H</i></b> = <input type="text" name="result_rect_h" size="10" maxlength="10">

           <SELECT name="hr_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1" selected>(A/m)</OPTION>
           <OPTION value="1e-3">(kA/m)</OPTION>
           <OPTION value="1e-2">(A/cm)</OPTION>
        </SELECT>
        
        
&nbsp;&nbsp;&nbsp;&nbsp;

<b><i>B</i></b>(μ<sub>0</sub>) = <input type="text" name="result_rect_b" size="10" maxlength="10">

           <SELECT name="br_unit" onChange="calculate_function3(this.form)">
           <OPTION value="1" selected>(T)</OPTION>
           <OPTION value="1e3">(mT)</OPTION>
           <OPTION value="1e6">(uT)</OPTION>
        </SELECT>

<br><br>
 </form>
 
</BODY>
<!-- ==================== calculator ends here ============== -->
</HTML>

//Notes: This is valid only for a uniformly magnetised cuboid magnet, for the field along its axis.[(Furlani>[[https://isbnsearch.org/isbn/0122699513|Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513]])] The value of B(μ<sub>0</sub>) is for vacuum. //

<box 100% #efffef>↑</box>
{{page>insert/paypal}}

{{tag>Magnetic_field_of_magnets Art Calculators}}