[Tex/LaTex] Putting Faraday’s law formula in LaTeX

math-modephysics

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

Best Answer

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}

Faraday’s Law

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}

Italic small caps sample

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.

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