You are asking how to use normal (ϵ), var (ε), and big epsilon (Ε) in LaTeX. I am explaining everything clearly and simply. I hope you will understand it well.
Normal epsilon symbol (ϵ)
This Greek letter is displayed using the \epsilon command. It is commonly seen in various problems in mathematics and physics. Let’s look at a perfect example to make it even clearer.
\[E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{q}{r^2}\]
\[E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{q}{r^2}\]
Var and big epsilon
If you want to see a slightly different form of the same letter, then use the \varepsilon command.
\[e^{x\varepsilon} = \sum_{n=0}^{\infty} \frac{(xn)^2}{n!}\]
\[e^{x\varepsilon} = \sum_{n=0}^{\infty} \frac{(xn)^2}{n!}\]
There is no default special command for Big epsilon; it looks almost 95% like the letter E, so the capital letter E is usually used.
If you want to use a command, you need to load the textgreek package, which contains the texEpsilon command. However, this command only works in text mode, not in math mode.
\mathcal{E} is not epsilon
Many use \mathcal{E} as var epsilon, but this is entirely incorrect. It is the calligraphic style of the letter E, typically used to denote electromotive force.
\[\mathcal{E} = \oint_{\mathcal{C}} \mathbf{E} \cdot d\mathbf{l}\]
\[ \mathcal{E} = \oint_{\mathcal{C}} \mathbf{E} \cdot d\mathbf{l} \]
Epsilon naught or permittivity
If you observe the symbol, it will be seen that a subscript zero is added. Use the ϵ command along with the subscript _0 to get the permittivity symbol.
\[ \epsilon_0 = \frac{1}{4 \pi} \cdot \frac{q_1 q_2}{F r^2} \]
\[ \epsilon_0 = \frac{1}{4 \pi} \cdot \frac{q_1 q_2}{F r^2} \]
