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 $$\mathbf{r}$$.

 

[astrokreng]

Dear Casey,

Yes, you are correct. Schey's notation for the electrostatic field is a shorthand way of representing the integral expression for the electric field at a given point \mathbf{r}. The primes indicate that the variables \rho, \hat{\mathbf{u}}, and dV are evaluated at different locations within the volume V. This notation is commonly used in electromagnetism to simplify the expression and avoid excessive subscripts. It is important to note that the integral is still evaluated over the entire volume V, but the notation allows for a more concise representation. I hope this clarifies any confusion you may have had.