# Putting Faraday's law formula in LaTeX

Can anyone tell me how to put the formula for faraday's law in LaTeX?

This is the formula I want

emf=(Delta.Phi)/(Delta.t)

thanks

• The Wikipedia version can be obtained with \documentclass{article} \begin{document} $\mathcal{E}=-\frac{\mathrm{d}\Phi_B}{\mathrm{d}t}$ \end{document}. – user121799 Jun 7 '19 at 0:26

It’s common to use ℰ (U+2130, or \mathcal{E}) as the symbol for EMF. There are a number of variations of Δ, but in unicode-math, stix or stix2, the upright math operator is \increment. In ISO style, both Φ and N are variables rather than constants, and so should be slanted. (Under the default settings, though, capital Greek letters appear upright.)

Here’s how I’d do that in the modern toolchain:

\documentclass[varwidth]{standalone}
\usepackage{mathtools}
\usepackage[math-style=ISO]{unicode-math}

\newcommand\Emf{\mathcal{E}}

\begin{document}
$\Emf = -N \frac{\increment \Phi}{\increment t}$
\end{document}


If you want to replace the symbol ℰ with the word Emf or EMF, replace the definition of \Emf with

\newcommand\Emf{\operatorname{Emf}}


This is spaced like the operator log or sin if you try to write something like 2 Emf t. (Eta: egreg correctly brings up that this breaks \Emf \cdot t, so you would need to insert a \! in front of a binary operator.)

If you want something visually distinct from either an operator or the product of variables named e, m and f, you might go with small caps:

\mathop{\text{\normalfont\scshape\selectfont emf}}


This departs from ISO style, in which variables are always slanted, unless you select slanted small caps, such as:

\documentclass[varwidth]{standalone}
\usepackage{mathtools}
\usepackage[math-style=ISO]{unicode-math}

\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{Libertinus Serif}[Scale = 1.0]
\setmathfont{Libertinus Math}

\newcommand\Emf{\mathop{\text{\normalfont\scshape\itshape\selectfont emf}}}

\begin{document}
$\Emf = -N \frac{\increment \Phi}{\increment t}$
\end{document}


If you prefer your capital Greek letters upright, remove the [math-style=ISO] option from \usepackage{unicode-math}.

If you’d rather have a slanted Δ, write \mathit{\Delta}.

If you have to (or prefer to) use PDFLaTeX instead of LuaLaTeX or XeLaTeX, load your font package of choice. Many math font packages have a slantedgreek option. If you aren’t using stix or stix2, you might replace \increment with either \Delta or \triangle.

• On the other hand, \operatorname{Emf}\cdot t would have wrong spacing. – egreg Jun 12 '19 at 22:02
• @egreg This is true, but {\mathrm{Emf}}t is even worse, in my opinion, and operatorname{Emf} \mathrel\cdot t is a decent workaround. No doubt there’s a more robust solution that you know about, but I don’t. – Davislor Jun 12 '19 at 22:28
• No, \operatorname{Emf}\mathrel\cdot t is not a decent workaround; quite the contrary. The correct spacing is obtained with \operatorname{Emf}{\!}\cdot t. Being the name of a variable, it should be \mathit{Emf}. – egreg Jun 12 '19 at 22:35
• @egreg Okay, that had been my second suggestion, but I edited to post your solution to the issue. My preference is for \mathcal{E}, but I think if I wanted to spell out EMF, I would do it as \mathop{\text{\textsc{Emf}}}. This is visually distinct from the product of variables E, m and f. I’m sure you know how to improve on that! – Davislor Jun 12 '19 at 23:02
• I came back and updated this answer because of a possible bug: changes to the style of the surrounding text bleed through to \text. In some cases, this might be desirable (e.g. if formulas in titles and headers should use bold math to match the text). In these cases, remove \normalfont and perhaps add \upshape. – Davislor Sep 18 '19 at 19:09

If you want a symbol, use \mathcal:

$\mathcal{E}=-N\frac{\Delta\mathnormal{\Phi}}{\Delta t}$


If you prefer “emf”, then it should be in italics like every other variable name:

$\mathit{emf}=-N\frac{\Delta\mathnormal{\Phi}}{\Delta t}$


Full example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$\mathcal{E}=-N\frac{\Delta\mathnormal{\Phi}}{\Delta t}$

$\mathit{emf}=-N\frac{\Delta\mathnormal{\Phi}}{\Delta t}$

\end{document}


• I’m dissatisfied with the second option There’s no visual cue at all that emf is an acronym and not a product of three variables. Worse, it has the default \mathord spacing, so bemf or emft will run together indecipherably. You have a point about italics, so I edited my answer to provide an alternative that solves these issues and also uses italic. – Davislor Jun 15 '19 at 8:11

For the emf, I will suggest to use mathalfa package with the calligraphic option cal=boondoxo. I have finded this symbol very similar to many Physics books.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[cal=boondoxo]{mathalfa}
\begin{document}
$\mathcal{E}=-N\frac{\Delta\Phi}{\Delta t}$
\end{document}


On page 122 of the guide of the symbols (The Comprehensive LATEX Symbol List) there are different options to obtain the emf symbol,

using emf package:

With this MWE I have used the fourier option.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
%\usepackage[boondox]{emf}
%\usepackage[calligra]{emf}
\usepackage[fourier]{emf}
%\usepackage[rsfs]{emf}

\begin{document}
$\emf=-N\frac{\Delta\Phi}{\Delta t}$
\end{document}

• Good choice. It is also very similar to the \mathcal{E}/\mscrE from XITS Math, if you use unicode-math instead. – Davislor Jun 15 '19 at 2:26
• @Davislor Thank you so much for your appreciation. You know I'm very sad that many of the best ones are wiping out from TeX.SE and I'm so sorry. My knowledge is very limited and I always hope that what I do is welcome. I always think that humility and fairness should be among the top places. Thanks again with all my heart. – Sebastiano Jun 15 '19 at 21:25

Your question is not very clear (for example which delta do you mean) but here one possibility:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

$\text{Emf} = \frac{\Delta\Phi}{\Delta t}$

\end{document}


and its result:

# Update:

Because the correct formula for faradays law has an -N added I corrected the code to the following mwe and added the comment of @Davislor in the second line:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

$\text{Emf} = - \mathrm{N} \frac{\Delta\Phi}{\Delta t}$

$\operatorname{Emf}=-\mathrm{N}\frac{\Delta\Phi}{\Delta t}$

\end{document}


and its result: