First and most important of all, the amount of hours you spend studying don't mean much by themselves, the way you spend them is what really matters.
If you find yourself distracted, and you've been at it for more than an hour, just take a break of 5 to 15 min. During your breaks splash some...
In the same way that this looks
\int (r_x,r_y,r_z) dx'dy'dz'
This is essentially the same as what's up there, just removed clutter. I don't understand how this works.
I understand the idea, but as a mathematical object it looks like nonsense to me. There are no examples in the textbook that use this formula directly. They use symmetry arguments such that only the magnitude of one direction is calculated.
I'm using the textbook Electricity and Magnetism by Purcell. In the section about continuous charge distributions I found the following formula
\mathbf{E}(x,y,z)= \frac{1}{4\pi\epsilon_0 } \int \frac{\rho(x',y',z')\boldsymbol{\hat r} dx'dy'dz'}{r^{2}} .
It's stated that (x,y,z) is fixed...