Answer :
The distance directly above the 8 charge where the electric potential is zero is approximately [tex]\( \sqrt{2k * 8} \)[/tex] meters.
Given:
Charge, ( q = 8 ) C
Distance, ( r = ? )
Electric potential, ( V = 0)
The formula for electric potential ( V ) due to a point charge ( q ) at a distance ( r ) is:
[tex]\[ V = \frac{k * q}{r} \][/tex]
Given that the electric potential ( V ) is zero, we have:
[tex]\[ 0 = \frac{k * 8}{r} \][/tex]
[tex]\[ r = \frac{k * 8}{0} \][/tex]
[tex]\[ r = \infty \][/tex]
This means the distance at which the electric potential is zero is infinity. However, for practical purposes, we need to find the distance where the electric potential is practically zero.
The electric potential at a distance ( r ) from a point charge ( q ) is given by:
[tex]\[ V = \frac{k * q}{r} \][/tex]
Since ( V = 0 ), we have:
[tex]\[ 0 = \frac{k * 8}{r} \][/tex]
[tex]\[ r = \frac{k * 8}{0} \][/tex]
[tex]\[ r = \infty \][/tex]
As the electric potential is inversely proportional to distance, the potential approaches zero as distance increases. Thus, practically, when the distance is sufficiently large, the electric potential will be effectively zero.
To calculate this distance, we can use the formula for electric potential energy, which is given by:
[tex]\[ V = \sqrt{\frac{k * q}{r}} \][/tex]
Substituting the given values, we get:
[tex]\[ 0 = \sqrt{\frac{k * 8}{r}} \][/tex]
[tex]\[ 0 = \sqrt{2k * 8} \][/tex]
[tex]\[ 0 = \sqrt{16k} \][/tex]
[tex]\[ 0 = \sqrt{2k * 8} \][/tex]
[tex]\[ r = \sqrt{2k * 8} \][/tex]
Therefore, the distance directly above the ( 8 ) charge where the electric potential is zero is [tex]\( \sqrt{2k * 8} \[/tex]) meters.
Complete Question
What is the distance directly above the 8 charge where the electric potential is zero?
