# Reason why dot notation isn't used for time derivatives in Maxwell's equations [closed]

Maxwell's equations seem to be usually written:

\begin{align} \nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\ \nabla \cdot \mathbf{B} &= 0,\\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t},\\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}, \end{align}

as opposed to

\begin{align} \nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\ \nabla \cdot \mathbf{B} &= 0,\\ \nabla \times \mathbf{E} &= -\dot{\mathbf{B}},\\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0\epsilon_0\dot{\mathbf{E}} \, . \end{align}

Is there any particular reason the more concise dot notation isn't used?

## closed as primarily opinion-based by Kyle Kanos, John Rennie, ZeroTheHero, stafusa, Jon CusterFeb 28 at 4:23

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

• There is no reason for it. Notation is a matter of preference, consistency and style. – flaudemus Feb 26 at 7:25
• @flaudemus Sure, but consider that Dirac notation is a matter of preference and yet (I think that) it's hard to deny that it's very useful. – PiKindOfGuy Feb 26 at 7:27
• In my experience the dot notation in almost only used in Newtonian physics (including analytic Newtonian physics). – Natanael Feb 26 at 7:28
• Could it be a will to insist on the fact that we have a partial differential here ? I believe the dot notation is used more widely as $\frac{d}{dt}$ than $\frac{\partial}{\partial t}$ – Barbaud Julien Feb 26 at 7:50
• @BarbaudJulien You should formulate it as an answer, as this is most likely the correct reason for the expression. – ahemmetter Feb 26 at 8:34

The dot notation typically refers to a total time derivative. In field theory partial & total time derivatives of the field are often the same, and the dot notation can sometimes be seen in the field theory literature as a convenient short-hand. An important exception is the material derivative in fluid dynamics. Similar ambiguities arise e.g. for a point particle $${\bf r}(t)$$ in an EM background, say an electric potential $$\phi$$, where the total and partial time derivative differ by a transport term $$\frac{d\phi({\bf r}(t),t)}{dt} ~=~\frac{\partial\phi({\bf r}(t),t)}{\partial t} + \dot{\bf r}(t)\cdot \nabla \phi({\bf r}(t),t).$$