Encyclopedia Magnetica™

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==== Calculator of inductance of a straight elliptical non-magnetic wire ====

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|  {{/calculator/icon_calc.png?60&nolink}}  | //[[user/Stan Zurek]], Calculator of inductance of a straight elliptical magnetic wire, Encyclopedia Magnetica//, \\ https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_elliptical_wire, {accessed: @YEAR@-@MONTH@-@DAY@} |
|  {{/wiki/logo.png?20&nolink}} //See more: [[/Calculators of inductance]]//  ||
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Definition of the dimensions of a **straight elliptical wire**
[[/file/inductance_of_straight_elliptical_wire_png|{{/inductance_of_straight_elliptical_wire.png}}]]
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[[/Inductance]] of a [[/straight wire]] or conductor made from [[/nonmagnetic material]] with elliptical cross-section can be calculated with the the equation as specified below. 

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

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

function calculate_function(frm){
// set up variables
var a          = frm.a.value
var b          = frm.b.value
var l          = frm.l.value
var result1    = "1"

var a_unit     = getSelectedValue(frm.a_unit)
var b_unit     = getSelectedValue(frm.b_unit)
var l_unit     = getSelectedValue(frm.l_unit)

var result1_unit    = getSelectedValue(frm.result1_unit)

const pi = 3.14159265358979
const u0 = 4e-7 * pi

// read values and convert to numbers
a = parseFloat(a)
b = parseFloat(b)
l = parseFloat(l)

l = l * l_unit

a = a * a_unit
b = b * b_unit

// calculate inductance
result1 = result1_unit * u0 * l * (Math.log(4*l/(a+b)) - 0.05685) / (2 * pi )

// format number to x digits precision, result will equal 1.234e+2
result1  = result1.toPrecision(5)

// display result
frm.result1.value = result1

}

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

<form method="post" action="">

 
<b>Wire diameter <i>a</i></b> = <input type="text" value="25.4" name="a" size="10" maxlength="10" onChange="calculate_function(this.form)">
        <SELECT name="a_unit" onChange="calculate_function(this.form)">
           <OPTION value="1">(m)</OPTION>
           <OPTION value="0.0254">(inch)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="1e-3" selected>(mm)</OPTION>
        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><br>

 
<b>Wire diameter <i>a</i></b> = <input type="text" value="6.35" name="b" size="10" maxlength="10" onChange="calculate_function(this.form)">
        <SELECT name="b_unit" onChange="calculate_function(this.form)">
           <OPTION value="1">(m)</OPTION>
           <OPTION value="0.0254">(inch)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="1e-3" selected>(mm)</OPTION>
        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><br>


<b>Wire length <i>l</i></b> = <input type="text" value="3048" name="l" size="10" maxlength="10" onChange="calculate_function(this.form)">  
        <SELECT name="l_unit" onChange="calculate_function(this.form)">
           <OPTION value="1">(m)</OPTION>
           <OPTION value="0.0254">(inch)</OPTION>
           <OPTION value="1e-2">(cm)</OPTION>
           <OPTION value="1e-3" selected>(mm)</OPTION>
        </SELECT> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><br>
   
        
<input type="button" name="Button" value="== Calculate ==" onClick="calculate_function(this.form)"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  
  
    <br><br>

<b><i>L</i></b> = <input type="text" name="result1" size="10" maxlength="10"> 
          <SELECT name="result1_unit" onChange="calculate_function(this.form)">
           <OPTION value="1">(H)</OPTION>
           <OPTION value="1e3">(mH)</OPTION>
           <OPTION value="1e6" selected>(μH)</OPTION>
           <OPTION value="1e9">(nH)</OPTION>
        </SELECT> <i>Grover, eq. (1)</i> <br>

 </form>

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

=== Equations ===

<WRAP lo>
//Note: Several assumptions are made for all these equations: 1) The return path is **not** considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than its diameter(s) (a,b << l), otherwise the calculation errors might be excessive. 3) The wire and the surrounding medium is assumed to be non-magnetic (μ<sub>r</sub> = 1). 4) The current is uniformly distributed inside the wire (no [[/skin effect]]). 5) The equations were converted here to be consistent with [[/SI units]].//
</WRAP>

<WRAP lo>
|< 100% >|
^  Inductance of a straight round magnetic wire or conductor  ^^^
| // Source: [2] F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570//  |||
|  **(1)** \\ //[2] Grover, eq. (10), p. 36//  |  $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{a+b} \right) - 0.05685 \right) $$  |  (H)  |
| where: $μ_0$ - [[/magnetic permeability of vacuum]] (H/m), $l$ - wire length (m), $a$, $b$ - shorted and longer diameters of ellipse (m)  |||
| //The original Grover's equation is expressed by "semiaxes" α, β  of the ellipse, with the under-logarithm coefficient as 2·l/(α+β), hence if the full "diameters" are used then this becomes 4·l/(a+b), as written above.//   |||
</WRAP>

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{{tag>Calculators Inductance_of_straight_wire Inductance_of_straight_conductor Elliptical_wire Elliptical_conductor}}