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Display information for equation id:math.224946.4 on revision:224946

* Page found: Magnetic dipole (eq math.224946.4)

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Hash: 55912e620a35e5ede1fd180f7b8c09ee

TeX (original user input):

\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\left[\frac{3\mathbf{n}(\mathbf{n}\cdot \mathbf{m})-\mathbf{m}}{|\mathbf{x}|^3} + \frac{8\pi}{3}\mathbf{m}\delta(\mathbf{x})\right],

TeX (checked):

\mathbf {B} (\mathbf {x} )={\frac {\mu _{0}}{4\pi }}\left[{\frac {3\mathbf {n} (\mathbf {n} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {x} |^{3}}}+{\frac {8\pi }{3}}\mathbf {m} \delta (\mathbf {x} )\right],

LaTeXML (experimental; uses MathML) rendering

MathML (10.923 KB / 1.667 KB) :

𝐁 ( 𝐱 ) = μ 0 4 π [ 3 𝐧 ( 𝐧 𝐦 ) - 𝐦 | 𝐱 | 3 + 8 π 3 𝐦 δ ( 𝐱 ) ] , 𝐁 𝐱 subscript 𝜇 0 4 𝜋 delimited-[] 3 𝐧 𝐧 𝐦 𝐦 superscript 𝐱 3 8 𝜋 3 𝐦 𝛿 𝐱 {\displaystyle{\mathbf{B}}({\mathbf{x}})={\frac{\mu_{0}}{4\pi}}\left[{\frac{3{% \mathbf{n}}({\mathbf{n}}\cdot{\mathbf{m}})-{\mathbf{m}}}{|{\mathbf{x}}|^{3}}}+% {\frac{8\pi}{3}}{\mathbf{m}}\delta({\mathbf{x}})\right],}
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SVG (14.979 KB / 4.696 KB) :

bold upper B times left-parenthesis bold x right-parenthesis equals StartFraction mu 0 Over 4 times pi EndFraction times left-bracket StartFraction 3 times bold n times left-parenthesis bold n dot bold m right-parenthesis minus bold m Over StartAbsoluteValue bold x EndAbsoluteValue cubed EndFraction plus StartFraction 8 times pi Over 3 EndFraction times bold m times delta times left-parenthesis bold x right-parenthesis right-bracket comma

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: B*(x)=(mu[0])/(4*pi)[(3*n*(n * m)- m)/((abs(x))^(3))+(8*pi)/(3)*m*delta*(x)],

Information about the conversion process:

\cdot: was translated to: *

\delta: Could be the first Feigenbaum constant.

But this system don't know how to translate it as a constant. It was translated as a general letter.


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.



Translation to Mathematica

In Mathematica: B*(x)=Divide[Subscript[\[Mu], 0],4*\[Pi]][Divide[3*n*(n * m)- m,(Abs[x])^(3)]+Divide[8*\[Pi],3]*m*\[Delta]*(x)],

Information about the conversion process:

\cdot: was translated to: *

\delta: Could be the first Feigenbaum constant.

But this system don't know how to translate it as a constant. It was translated as a general letter.


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.



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