Recent content by jmwilli25

- (\vec{m}\cdot\nabla)\left[\frac{\vec{x}}{|\vec {x}|^3}\right]= -{\vec x} ({\vec m}\cdot\nabla)\frac{1}{|{\vec x}|^3} -\frac{1}{|{\vec x}|^3} ({\vec m}\cdot\nabla){\vec x}

I figured it out! You have to use what is called the dyadic. The unit dyadic is 1=ii+jj+kk

Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...

Sorry, it is the partial derivative inside the integral and \delta(\vec{r}-\vec{R}(t)) is the dirac delta function. Context: I am trying to show that the equation of charge conservation holds when \rho(\vec{r},t)=e\delta(\vec{r}-\vec{R}(t)) The entire equation that I am trying to solve is...

Homework Statement I just need help integrating this equation. e is just the charge of an electron so it is constant Homework Equations -\int_{V}d\vec{r}\frac{\delta}{\delta t}e\delta(\vec{r}-\vec{R}(t)) The Attempt at a Solution...