I am having a trouble with the existence of "uniform electric field". As far as I know, the electric field is measured with two main formulas:
1) $E=k\frac{\left | Q \right |}{r^{{2}}}$
2) $E=\frac{F}{q}$
However, what I don't stand is that $E$ and $r^{2}$ in this relationship make the eletric field change followed by distance. I have read and get mentioned about infinite line of charge but I still don't understand. I just know that:
1) The uniform with electric field (don't know the specific formula) use $r$ instead of $r^{2}$. That's why the eletric field doesn't change according to distance.
2) The Coulomb's law however applying on sphere charged object. And we get $r^{2}$. But I don't know why we have such formula (where the formula derive from ?)
Is there a simple way to comprehend this matter?
Best Answer
Maybe this analogy might help: The earth's gravitational field is almost constant near the surface, even though we know its equation depends on r^2:
$$ \vec{g} = \frac{\vec{F}}{m} = -GM\frac{\hat{R}}{R^2} $$
Very close to the surface it seems that the surface is infinitely long. When you look at the gravitational field of tiny masses and take their sum (keeping in mind that your surface extends infinitely), all components will cancel except for the vertical component. This is why gravity is pretty much constant on the surface of the earth.
The same can be said about two parallel plates. If we use the simple model that electrons are particles on the surface of such plates, the same model applies. We can sum the electric field of each particle to find that only the vertical components remain, and the field is then uniform.