Answer:
![\sigma=2.124\times 10^{-13}C/m^{2}](https://tex.z-dn.net/?f=%5Csigma%3D2.124%5Ctimes%2010%5E%7B-13%7DC%2Fm%5E%7B2%7D)
Explanation:
Given:
Electric Flux = ![3\times10^{-5}N.m^2/C](https://tex.z-dn.net/?f=3%5Ctimes10%5E%7B-5%7DN.m%5E2%2FC)
Side of sheet = 5cm
Area of the square sheet, A= 5×5 = 25cm²=25×10⁻⁴ m²
Now
the electric flux (Φ) is given as:
![\phi =EA](https://tex.z-dn.net/?f=%5Cphi%20%3DEA)
where, E = Electric field
or
![E=\frac{\phi}{A}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B%5Cphi%7D%7BA%7D)
substituting the values in the above equation, we get
![E=\frac{3\times10^{-5}N.m^2/C}{25\times 10^{-4}}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B3%5Ctimes10%5E%7B-5%7DN.m%5E2%2FC%7D%7B25%5Ctimes%2010%5E%7B-4%7D%7D)
![E=0.012N/C](https://tex.z-dn.net/?f=E%3D0.012N%2FC)
Now the charge density (σ) on a sheet is given as:
![\sigma=2\epsilon_oE](https://tex.z-dn.net/?f=%5Csigma%3D2%5Cepsilon_oE)
where,
= Permittivity of the free space = 8.85×10⁻¹²
substituting the values in the above equation, we get
![\sigma=2\times 8.85\times10^{-12}\times 0.012](https://tex.z-dn.net/?f=%5Csigma%3D2%5Ctimes%208.85%5Ctimes10%5E%7B-12%7D%5Ctimes%200.012)
![\sigma=2.124\times 10^{-13}C/m^{2}](https://tex.z-dn.net/?f=%5Csigma%3D2.124%5Ctimes%2010%5E%7B-13%7DC%2Fm%5E%7B2%7D)
Answer:
a.) The main scale reading is 10.2cm
b.) Division 7 = 0.07
c.) 10.27 cm
d.) 10.31 cm
e.) 10.24 cm
Explanation:
The figure depicts a vernier caliper readings
a.) The main scale reading is 10.2 cm
The reading before the vernier scale
b.) Division 7 = 0.07
the point where the main scale and vernier scale meet
c.) The observed readings is
10.2 + 0.07 = 10.27 cm
d.) If the instrument has a positive zero error of 4 division
correct reading = 10.27 + 0.04 = 10.31cm
e.) If the instrument has a negative zero error of 3 division
correct reading = 10.27 - 0.03 = 10.24cm
Answer:
![e=3367.2J](https://tex.z-dn.net/?f=e%3D3367.2J)
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Explanation:
From the exercise we know two information. The real speed and the experimental measured by the speedometer
![v_{r}=10km/h=2.77m/s](https://tex.z-dn.net/?f=v_%7Br%7D%3D10km%2Fh%3D2.77m%2Fs)
Since the speedometer is only accurate to within 0.1km/h the experimental speed is
![v_{e}=10km/h-0.1km/h=9.9km/h=2.75m/s](https://tex.z-dn.net/?f=v_%7Be%7D%3D10km%2Fh-0.1km%2Fh%3D9.9km%2Fh%3D2.75m%2Fs)
Knowing that we can calculate Kinetic energy for the real and experimental speed
![E_{r}=\frac{1}{2}mv^2=\frac{1}{2}(61000g)(2.77m/s)^2=234023J](https://tex.z-dn.net/?f=E_%7Br%7D%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2%3D%5Cfrac%7B1%7D%7B2%7D%2861000g%29%282.77m%2Fs%29%5E2%3D234023J)
![E_{e}=\frac{1}{2}mv^2=\frac{1}{2}(61000g)(2.75m/s)^2=230656J](https://tex.z-dn.net/?f=E_%7Be%7D%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2%3D%5Cfrac%7B1%7D%7B2%7D%2861000g%29%282.75m%2Fs%29%5E2%3D230656J)
Now, the potential error in her calculated kinetic energy is:
![e=E_{r}-E_{e}=(234023-230656)J=3367.2J](https://tex.z-dn.net/?f=e%3DE_%7Br%7D-E_%7Be%7D%3D%28234023-230656%29J%3D3367.2J)
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