Answer :
Answer:
The distance is [tex]z = \frac{1 + \sqrt{ \frac{k * q_2 }{ k * q_1}}}{s}[/tex]
Explanation:
From the question we are told that
The positive charges is [tex]q_1 \ and \ q_2[/tex]
The distance of separation is [tex]s[/tex]
Generally at the point where the electric field is zero would be a point where
The electric field due to [tex]q_1[/tex] = The electric field due to [tex]q_2[/tex]
Generally the electric field due to [tex]q_1[/tex] is mathematically represented as
[tex]E_1 = \frac{k * q_1}{ z^2 }[/tex]
Since we are taking our reference from [tex]q_1[/tex] then the electric field due to [tex]q_2[/tex] is mathematically represented as
[tex]E_2 = \frac{k * q_2}{ (s- z)^2 }[/tex]
So
[tex]\frac{k * q_1}{ z^2 } = \frac{k * q_2}{ (s- z)^2 }[/tex]
[tex]k * q_1 * (s- z)^2= k * q_2 * z^2[/tex]
[tex][ \frac{s -z }{z} ]^2 = \frac{k * q_2 }{ k * q_1}[/tex]
[tex]\frac{s -z }{z} = \sqrt{ \frac{k * q_2 }{ k * q_1}}[/tex]
[tex]\frac{s}{z} - 1 = \sqrt{ \frac{k * q_2 }{ k * q_1}}[/tex]
[tex]z = \frac{1 + \sqrt{ \frac{k * q_2 }{ k * q_1}}}{s}[/tex]