Answer:
E = 1580594.95 N/C
Explanation:
To find the electric field inside the the non-conducting shell for r=11.2cm you use the Gauss' law:
(1)
dS: differential of the Gaussian surface
Qin: charge inside the Gaussian surface
εo: dielectric permittivity of vacuum = 8.85 × 10-12 C2/N ∙ m2
The electric field is parallel to the dS vector. In this case you have the surface of a sphere, thus you have:
(2)
Qin is calculate by using the charge density:
(3)
Vin is the volume of the spherical shell enclosed by the surface. a is the inner radius.
The charge density is given by:
![\rho=\frac{Q}{V}=\frac{13*10^{-6}C}{\frac{4}{3}\pi((0.15m)^3-(0.10m)^3)}\\\\\rho=1.30*10^{-3}\frac{C}{m^3}](https://tex.z-dn.net/?f=%5Crho%3D%5Cfrac%7BQ%7D%7BV%7D%3D%5Cfrac%7B13%2A10%5E%7B-6%7DC%7D%7B%5Cfrac%7B4%7D%7B3%7D%5Cpi%28%280.15m%29%5E3-%280.10m%29%5E3%29%7D%5C%5C%5C%5C%5Crho%3D1.30%2A10%5E%7B-3%7D%5Cfrac%7BC%7D%7Bm%5E3%7D)
Next, you use the results of (3), (2) and (1):
![E(4\pi r^2)=\frac{4}{3\epsilon_o}(r^3-a^3)\rho\\\\E=\frac{\rho}{3\epsilo_o}(r-\frac{a^3}{r^2})](https://tex.z-dn.net/?f=E%284%5Cpi%20r%5E2%29%3D%5Cfrac%7B4%7D%7B3%5Cepsilon_o%7D%28r%5E3-a%5E3%29%5Crho%5C%5C%5C%5CE%3D%5Cfrac%7B%5Crho%7D%7B3%5Cepsilo_o%7D%28r-%5Cfrac%7Ba%5E3%7D%7Br%5E2%7D%29)
Finally, you replace the values of all parameters, and for r = 11.2cm = 0.112m you obtain:
![E=\frac{1.30*10^{-3}C/m^3}{3(8.85*10^{-12}C^2/Nm^2)}((0.112m)-\frac{(0.10)^3}{(0.112m)^2})\\\\E=1,580,594.95\frac{N}{C}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1.30%2A10%5E%7B-3%7DC%2Fm%5E3%7D%7B3%288.85%2A10%5E%7B-12%7DC%5E2%2FNm%5E2%29%7D%28%280.112m%29-%5Cfrac%7B%280.10%29%5E3%7D%7B%280.112m%29%5E2%7D%29%5C%5C%5C%5CE%3D1%2C580%2C594.95%5Cfrac%7BN%7D%7BC%7D)
hence, the electric field is 1580594.95 N/C
Explanation:
Initial speed of the rocket, u = 0
Acceleration of the rocket, ![a=25.4\ m/s^2](https://tex.z-dn.net/?f=a%3D25.4%5C%20m%2Fs%5E2)
Time taken, t = 3.39 s
Let v is the final velocity of the rocket when it runs out of fuels. Using the equation of kinematics as :
![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
Let x is the initial position of the rocket. Using third equation of kinematics as :
![v^2=u^2+2ax_o](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2B2ax_o)
![x_o=\dfrac{v^2}{2a}](https://tex.z-dn.net/?f=x_o%3D%5Cdfrac%7Bv%5E2%7D%7B2a%7D)
Let
is the position at the maximum height. Again using equation of motion as :
![v^2-u^2=2a(x-x_o)](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2a%28x-x_o%29)
Now
and v and u will interchange
![u^2=2g(x-x_o)](https://tex.z-dn.net/?f=u%5E2%3D2g%28x-x_o%29)
![x=x_o+\dfrac{u^2}{2g}](https://tex.z-dn.net/?f=x%3Dx_o%2B%5Cdfrac%7Bu%5E2%7D%7B2g%7D)
![x=145.92+\dfrac{(86.10)^2}{2\times 9.8}](https://tex.z-dn.net/?f=x%3D145.92%2B%5Cdfrac%7B%2886.10%29%5E2%7D%7B2%5Ctimes%209.8%7D)
x = 524.14 meters
Hence, this is the required solution.
<u>Answer</u>
0.00346 hL
<u>Explanation</u>
cL means Centilitre while hL means Hectolitre.
10,000 cL = 1 hL
∴ 34.6 cL = 34.6/10,000 hL
= <em>0.00346 hL</em>
Answer:
Distance =60m, Time = 6s, Speed = ?
Speed = distance/time
= 60/6
=10m/s
Explanation:
Hope that this is helpful.
Have a nice day.
Answer:
You need to write an essay with 800 to 1,200 words. That talks about the significance of one of the seminal works (Definition- a work that strongly influenced people. Example: Martin Luther King Jr's speech "I Have A Dream") in the unit and how it connects to current issues (Example- Politics). It should be clearly stated and should be well supported by research (Example- a trustworthy article talking about its influence). You should properly cite at least 3 good sources from different perspectives. (Example- a republicans view for one source, a democratic for another, and a neutral for the third) You should also use direct quotes (Example: "Let them eat cake." - Marie Antoinette) and paraphrase- put it in your own words. (Example: Marie Antoinette said that they should eat cake.) I hope this helps, good luck! :)
Explanation: