Electrostatic FieldSchey's Notation

[Saladsamurai]

Hey there,

I am just seeking some clarification wrt the notation that I have come across for the Electrostatic Field:

$$\mathvf{E}(\mathbf{r})=\frac{1}{4\pi\epsilon_0}\int\int\int_V\frac{\rho(\mathbf{r'})\hat{\mathbf{u}}(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^2}\,dV'$$

So are all of the 'primes' just saying that the $\rho,\hat{u}, dV$ are simply those that correspond to the same location?

It seems like it is just a 'shorthand' notation to avoid a bunch of subscripts.

Is this correct?

Thanks,
Casey

 

[physicsworks]

All the "primes" are correspond to the source $$dq$$ of your (continuous) charge distribution, when $$\mathbf{r}$$ corresponds to the filed point, i.e. the point, where you want to find $$\mathbf{E}$$.
$$|\mathbf{r}-\mathbf{r'}|$$ is simply the distance between the source $$dq$$ and the field point $$\mathbf{r}$$.