Answer:
122.84 J
Explanation:
Since plate is square, area, A is given by ![(8.7/100)^{2}=0.007569m^{2}](https://tex.z-dn.net/?f=%288.7%2F100%29%5E%7B2%7D%3D0.007569m%5E%7B2%7D)
The distance between plates, d, is given in the question as 2mm=0.002m
Charge on plate, Q, as given in the question is 240 ![\mu c](https://tex.z-dn.net/?f=%5Cmu%20c)
Assuming mica dielectric constant, k of 7
Capacitance, C is given by
C=![\frac {k\epsilon_{o}A}{d}=\frac {(7)(8.85*10^{-12})(0.007569)}{0.002}=2.34*10*^{-10}F](https://tex.z-dn.net/?f=%5Cfrac%20%7Bk%5Cepsilon_%7Bo%7DA%7D%7Bd%7D%3D%5Cfrac%20%7B%287%29%288.85%2A10%5E%7B-12%7D%29%280.007569%29%7D%7B0.002%7D%3D2.34%2A10%2A%5E%7B-10%7DF)
Stored energy, E is given by
E=![\frac {Q^{2}}{2C}=\frac {(240*10^{-6})^{2}}{2*(2.34*10^{-10})}=122.84J](https://tex.z-dn.net/?f=%5Cfrac%20%7BQ%5E%7B2%7D%7D%7B2C%7D%3D%5Cfrac%20%7B%28240%2A10%5E%7B-6%7D%29%5E%7B2%7D%7D%7B2%2A%282.34%2A10%5E%7B-10%7D%29%7D%3D122.84J)
Therefore, the stored energy is 122.84 J
Answer:
a) 3.37 x ![10^{3} kg/m^3](https://tex.z-dn.net/?f=10%5E%7B3%7D%20kg%2Fm%5E3)
b) 6.42kg/![m^{3}](https://tex.z-dn.net/?f=m%5E%7B3%7D)
Explanation:
a) Firstly we would calculate the volume of the metal using it`s weight in air and water , after finding the weight we would find the density .
Weight of metal in air = 50N = mg implies the mass of metal is 5kg.
Now the difference of weight of the metal in air and water = upthrust acting on it = volume (metal) p (liquid) g = V (1000)(10) = 14N. So volume of metal piece = 14 x
. So density of metal = mass of metal / volume of metal = 5 / 14 x
= 3.37 x ![10^{3} kg/m^3](https://tex.z-dn.net/?f=10%5E%7B3%7D%20kg%2Fm%5E3)
b) Water exerts a buoyant force to the metal which is 50−36 = 14N, which equals the weight of water displaced. The mass of water displaced is 14/10 = 1.4kg Since the density of water is 1kg/L, the volume displaced is 1.4L. Hence, we end up with 3.57kg/l. Moreover, the unknown liquid exerts a buoyant force of 9N. So the density of this liquid is 6.42kg/![m^{3}](https://tex.z-dn.net/?f=m%5E%7B3%7D)
![\boxed{\sf C=\dfrac{Q}{V}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20C%3D%5Cdfrac%7BQ%7D%7BV%7D%7D)
But
![\boxed{\sf \Delta V_{R_2\to R_1}={\displaystyle{\int}^{R_1}_{R_2}}dV=-{\displaystyle{\int}^{R_1}_{R_2}}\dfrac{kQ}{r^2}dR}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5CDelta%20V_%7BR_2%5Cto%20R_1%7D%3D%7B%5Cdisplaystyle%7B%5Cint%7D%5E%7BR_1%7D_%7BR_2%7D%7DdV%3D-%7B%5Cdisplaystyle%7B%5Cint%7D%5E%7BR_1%7D_%7BR_2%7D%7D%5Cdfrac%7BkQ%7D%7Br%5E2%7DdR%7D)
- Hence higher the radius lower the voltage
- Lower the voltage higher the capacitance .
<h3>100cm diameter having aluminium sphere has a larger capacitance</h3>
<span>You experience physiological changes and a feeling of fear simultaneously. Hope this helped!</span>