# Tagged Questions

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### Why do we assume electromagnetic fields to be doubly differentiable? [duplicate]

It seems like the identities of curl of gradient, divergence of curl, and the simple derivations of electromagnetic waves from Maxwell equations all rely on the symmetry (interchangeability of their ...
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### Meaning of $\nabla_{\mathbf{p}_k} W(\mathbf p, h)$ in PBF

I'm reading this paper on Position Based Fluids and I couldn't understand the meaning of $\nabla_{\mathbf{p}_k} W(\mathbf{ p_i - p_j}, h)$ in the equation 7 (see below). …the gradient of the ...
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### Derivation of centripetal acceleration

While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
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### Maximum electric field of a circular ring

How do you differentiate the equation for electric field of uniform ring $$E_x = \frac{kxQ}{(x^2+r^2)^{3/2}}$$to get the maximum at a point? My book says $x = \frac{r}{\sqrt2}$. I tried ...
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### Covariant derivative of a covariant derivative

I'm trying to find the covariant derivative of a covariant derivative, i.e. $\nabla_a (\nabla_b V_c)$. This is something I've taken for granted a lot in calculations, namely I though that by the ...
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### Is $\dfrac{dx}{dt}$ a fraction or not?

I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that $\dfrac{dx}{dt}$ ...
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### Vector Derivative: General Case

From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector". In this section, towards the ...
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### Differential Operator

I am trying to understand the following expression \begin{eqnarray} e^{-ik.x}D_{\mu}D^{\mu}e^{ik.x} & = & e^{-ik.x}(i\partial_{\mu}+A_{\mu})(i\partial^{\mu}+A^{\mu})e^{ik.x}\\ & = & e^{...
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### Directional derivative of the potential energy in the direction of the displacement in three dimensions

For a conservative force $\vec{F}=-\vec{\nabla } U \implies \mathrm dW= -\vec{\nabla} U \cdot \mathrm d\vec{s}$ Where $\mathrm d\vec{s}$ is the infinitesimal displacement. For a differentiable ...
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### Infinitesimal time intervals use

I've a question, that maybe will sound obvious, on the use of infinitesimal quantities. Consider the expression for the acceleration in non inertial frames. \$\frac{d\vec{v}}{dt}=\frac{d\vec{v'}}{dt}...