Its when the animal repeats what it is taught similar to a child you never really teach them to lie it just happens because they have seen other people do it
Answer:
![|\vec{F}| = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}(\ln(L+x_0)-\ln(x_0))](https://tex.z-dn.net/?f=%7C%5Cvec%7BF%7D%7C%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7BqQ%7D%7BL%7D%28%5Cln%28L%2Bx_0%29-%5Cln%28x_0%29%29)
Explanation:
The force on the point charge q exerted by the rod can be found by Coulomb's Law.
![\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\^r](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7Bq_1q_2%7D%7Br%5E2%7D%5C%5Er)
Unfortunately, Coulomb's Law is valid for points charges only, and the rod is not a point charge.
In this case, we have to choose an infinitesimal portion on the rod, which is basically a point, and calculate the force exerted by this point, then integrate this small force (dF) over the entire rod.
We will choose an infinitesimal portion from a distance 'x' from the origin, and the length of this portion will be denoted as 'dx'. The charge of this small portion will be 'dq'.
Applying Coulomb's Law:
![d\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{qdq}{x + x_0}(\^x)](https://tex.z-dn.net/?f=d%5Cvec%7BF%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7Bqdq%7D%7Bx%20%2B%20x_0%7D%28%5C%5Ex%29)
The direction of the force on 'q' is to the right, since both charges are positive, and they repel each other.
Now, we have to write 'dq' in term of the known quantities.
![\frac{Q}{L} = \frac{dq}{dx}\\dq = \frac{Qdx}{L}](https://tex.z-dn.net/?f=%5Cfrac%7BQ%7D%7BL%7D%20%3D%20%5Cfrac%7Bdq%7D%7Bdx%7D%5C%5Cdq%20%3D%20%5Cfrac%7BQdx%7D%7BL%7D)
Now, substitute this into 'dF':
![d\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{qQdx}{L(x+x_0)}(\^x)](https://tex.z-dn.net/?f=d%5Cvec%7BF%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7BqQdx%7D%7BL%28x%2Bx_0%29%7D%28%5C%5Ex%29)
Now we can integrate dF over the rod.
![\vec{F} = \int{d\vec{F}} = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}\int\limits^{L}_0 {\frac{1}{x+x_0}} \, dx = \frac{1}{4\pi\epsilon_0}\frac{qQ}{L}(\ln(L+x_0)-\ln(x_0))(\^x)](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%20%3D%20%5Cint%7Bd%5Cvec%7BF%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7BqQ%7D%7BL%7D%5Cint%5Climits%5E%7BL%7D_0%20%7B%5Cfrac%7B1%7D%7Bx%2Bx_0%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7BqQ%7D%7BL%7D%28%5Cln%28L%2Bx_0%29-%5Cln%28x_0%29%29%28%5C%5Ex%29)
Answer:
The capacitance of the deflecting plates is
.
Explanation:
The expression for the capacitance of the capacitor in terms of area and distance is as follows;
![C=\frac{\varepsilon _{0}A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cvarepsilon%20_%7B0%7DA%7D%7Bd%7D)
Here, C is the capacitance, A is the area, d is the distance and
is the absolute permittivity.
Convert the side of the square from cm to m.
s= 3.0 cm
s= 0.030 m
Calculate the area of the square.
![A= s_^{2}](https://tex.z-dn.net/?f=A%3D%20s_%5E%7B2%7D)
Put s= 0.030 m.
![A=(0.030)_^{2}](https://tex.z-dn.net/?f=A%3D%280.030%29_%5E%7B2%7D)
![A=9\times10^{-4}m^{-2}](https://tex.z-dn.net/?f=A%3D9%5Ctimes10%5E%7B-4%7Dm%5E%7B-2%7D)
Convert distance from mm to m.
d= 5.0 mm
![d=5\times10^{-3}m](https://tex.z-dn.net/?f=d%3D5%5Ctimes10%5E%7B-3%7Dm)
Calculate the capacitance of the deflecting plates.
![C=\frac{\varepsilon _{0}A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cvarepsilon%20_%7B0%7DA%7D%7Bd%7D)
Put
,
and
.
![C=\frac{(8.85\times 10^{-12})(9\times10^{-4})}{5\times10^{-3}}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%288.85%5Ctimes%2010%5E%7B-12%7D%29%289%5Ctimes10%5E%7B-4%7D%29%7D%7B5%5Ctimes10%5E%7B-3%7D%7D)
![C=1.59\times 10^{-12}F](https://tex.z-dn.net/?f=C%3D1.59%5Ctimes%2010%5E%7B-12%7DF)
![C=1.59 pF](https://tex.z-dn.net/?f=C%3D1.59%20pF)
Therefore, the capacitance of the deflecting plates is
.
Answer:
It would because the shape of the rocket is designed to be able to slice through the air as smooth as possible and now you may be thinking that air is already smooth but when you try to push something as large and heavy like a rocket then the shape of the rocket will be very important. The bottom of the rocket is flatter then the top so it is not designed to fly smoothly through the air. So the rocket would fall vertically downward(If it was still in one piece)because of it's shape. It is easier for the top of the rocket to go smoothly through the air then the bottom.
Explanation:
I am 90% sure this is correct but if I'm not please tell me