# All Questions

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### Divergence of $\frac{ \hat {\bf r}}{r^2}$ , what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2}$ , now from the book, Griffiths says: Now what is the paradox, exactly? ...
144 views

### Mathematical rigorous definition for an electrical dipole

I've been reading Laurent Schwartz's Mathematics for the physical sciences, and in the chapter on distributions he makes many cool examples of ways to define in a mathematical rigorous way certain ...
44 views

### Is it true that any electrostatic charge density can be represented by Dirac Delta function? Give me a general example

My college professor said that any charge density can be replaced by Dirac Delta function but how I want to know.
27 views

### What is the volume charge density (in spherical coordinates)?

What is the volume charge density (in spherical coordinates) of a uniform, in finitesimally thin spherical shell of radius $R$ and total charge $Q$, centered at the origin? Give your answer in terms ...
45 views

### What is dipolar charge distribution?

An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains ...
66 views

### Integrating Laplace's equation over a sphere

The Wikipedia page on Laplace's equation states that if the Laplacian of $u$ is integrated over any volume that encloses the source point, $$\iiint_V \nabla \cdot \nabla u \, d^3V =-1.$$ I can'...
79 views

79 views

### Is the static electric field $\vec{E}$ defined and finite where charges are located?

Suppose you have a continuous charge distribution, e.g. a wire, a disk, or a plane, represented by a subset $D\subset \mathbb{R^3}$. The charge density is $\rho: \mathbb{R^3}\rightarrow \mathbb{R}$. ...
### The charge density $\rho_{\infty}$ of the sphere
I have two charged hemispheres (which are very close to each other, we consider them now as a sphere) with the charge density given as $\rho = \frac {Q}{\pi a^3 \frac {4}{3+n}} (\frac{r}{a})^n$, ...