Answer:
The line charge density is ![1.59\times10^{-4}\ C/m](https://tex.z-dn.net/?f=1.59%5Ctimes10%5E%7B-4%7D%5C%20C%2Fm)
Explanation:
Given that,
Diameter = 2.54 cm
Distance = 19.6 m
Potential difference = 115 kV
We need to calculate the line charge density
Using formula of potential difference
![V=EA](https://tex.z-dn.net/?f=V%3DEA)
![V=\dfrac{\lambda}{2\pi\epsilon_{0}r}\times\pi r^2](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_%7B0%7Dr%7D%5Ctimes%5Cpi%20r%5E2)
![\lambda=\dfrac{V\times2\epsilon_{0}}{r}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7BV%5Ctimes2%5Cepsilon_%7B0%7D%7D%7Br%7D)
Where, r = radius
V = potential difference
Put the value into the formula
![\lambda=\dfrac{115\times10^{3}\times2\times8.8\times10^{-12}}{1.27\times10^{-2}}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7B115%5Ctimes10%5E%7B3%7D%5Ctimes2%5Ctimes8.8%5Ctimes10%5E%7B-12%7D%7D%7B1.27%5Ctimes10%5E%7B-2%7D%7D)
![\lambda=1.59\times10^{-4}\ C/m](https://tex.z-dn.net/?f=%5Clambda%3D1.59%5Ctimes10%5E%7B-4%7D%5C%20C%2Fm)
Hence, The line charge density is ![1.59\times10^{-4}\ C/m](https://tex.z-dn.net/?f=1.59%5Ctimes10%5E%7B-4%7D%5C%20C%2Fm)
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And because of gravity it falls back down to the earth.