In a capacitor, for this formula
$$ C = \epsilon \frac{A}{d}$$
dielectric constant is calculated using
$$ \epsilon_{eff} = \frac{\int\epsilon dV}{V} $$
or in 2D
$$ \epsilon_{eff} = \frac{\int\epsilon dA}{A} $$
I know capacitors are full of approximations but there is this formula and I don't...
Coulomb's Law $$ \vec{F} = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r^2} \hat{r} $$
$$ \vec{E} = \frac{1}{4 \pi \epsilon} \frac{Q}{r^2} \hat{r} $$
Let's say we want to find electric field with a distance r from charge Q. How does permittivity effects the magnitude? Will I choose the permittivity...
Must object and its image be on the same line that is perpendicular to the surface? And why? Actually that's what all I need to know. If yes (1) is correct (2) is wrong, if no (1) is wrong (2) is correct.
(Black one is the object and grey is its image.)
We know from Snell's Law:
$$
n_1\sin\alpha=n_2\sin\theta
$$
And I have been said that:
$$
a=b\ (1)\\\ and\\\ \frac{h}{h'}=\frac{n_2}{n_1} \ (2)
$$
Let's begin.
$$...
I wrote
$$a_c=\frac{T}{m}$$
But it must be equal to
$$a_c=\frac{T+mgcos(\theta)}{m}$$
Actually I mistakenly used T as the centripetal force. It can easily be replaced. I just wanted to fix that.
I have a pendulum and an object with radius "R" and mass "m". There are forces: constant gravitational acceleration and tension on the rope. I can write:
$$x=R sin(\theta) \ \ y=R cos(\theta)$$
$$\dot{x}=R\dot{\theta}cos(\theta) \ \ \dot{y}=-R\dot{\theta}sin(\theta)$$...
I don't care my power consumption. But I got what I was chasing I think, thank you for that. It was just about definition. I constructed it on power.
$$ε(t)=ε_{max}sin(\omega t)$$
$$P(t)=\frac{{ε_{max}}^2 sin^2(\omega t)}{R}$$...