The curl in cylindrical coordinates is defined: $$\nabla \times \vec{A}=\left({\frac {1}{\rho }}{\frac {\partial A_{z}}{\partial \varphi }}-{\frac {\partial A_{\varphi }}{\partial z}}\right){\hat {\... 4answers 55k views ### Divergence of a field and its interpretation The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ... 4answers 16k views ### How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that? On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ... 3answers 2k views ### The magnetic field of a magnetic monopole Let us define the magnetic field$$\vec{B} = g\frac{\vec{r}}{r^3}$$for some constant g. How can we show that the divergence of this field correspond to the charge distribution of a single magnetic ... 6answers 6k views ### What is the origin of the Dirac delta term in the dipole electric field? I am a bit lost how one has deduced the formula for electric field with electric dipole because of some inconsistency between different sources. The Wikipedia article contains a delta function in the ... 4answers 316 views ### What's the commutator of |\mathbf{\hat{x}}| and |\mathbf{\hat{p}}|? [closed] Straight to the point: what's the result of the commutator of the magnitude of the position and the momentum operators and how can I approach it, i.e., [|\mathbf{\hat{x}}|,|\mathbf{\hat{p}}|]= ? My ... 1answer 2k views ### If the electrostatic Coulomb force followed inverse cube law, what's implication on Gauss' law? If the electrostatic force between two charged particles varied according to the inverse of the cube of distance between them, how would it affect the Gauss Law? Well we know if a metallic sphere is ... 1answer 540 views ### Differentiation and delta function Need help doing this simple differentiation. Consider 4 d Euclidean(or Minkowskian) spacetime. $$\partial_{\mu}\frac{(a-x)_\mu}{(a-x)^4}= ?$$ where a_\mu is a constant ... 1answer 218 views ### How to derive the \frac{4\pi}{3}\vec{p}\delta^3(\vec{r}) element for the dipole field, from its potential? This might be a bit more general question about how to figure out what is the appropriate (delta) expression in singular points, but e.g. for the dipole, we can derive its potential by a taylor ... 1answer 758 views ### Differentiating the electric field in Gauss's law, I get zero charge density. Can anyone help me where am I going wrong?$$\mathbf E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2} \mathbf e_r\nabla \cdot\mathbf E = \frac{\rho_V}{\epsilon}\begin{align} \implies \nabla\cdot\mathbf E & = \frac{1}{r^2}\frac{\partial}{\... 1answer 484 views ### Distributions (e.g., Dirac Delta): confused and unhappy [closed] I am sorry that the following set of questions is very fuzzy and ill informed. I am a trained mathematician and now studying an undergraduate theoretical physics course. We use distributions. I have ... 3answers 280 views ### Verify that the electrostatic potential satisfies the Poisson equation [closed] I'm reading Sect1.7 of Jackson's classical electrodynamics but I have trouble following his argument. Could someone help explain how exactly the Laplacian is evaluated in 1.30? Is it calculated with ... 0answers 53 views ### Dirac delta function equation intuition and proof [duplicate] What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation.{\nabla \cdot \Bigg ( \frac{\vec{s}}{|\vec{s}...
While solving for the curl of the magnetic field($\vec \nabla\times \vec B = \mu_0 \vec J$), I got one formula which is written as \vec \nabla \cdot \frac{\hat r}{r^2} = 4\pi \delta^3 \vec r \tag{1}\$...