Answer:
The locus of points where the electric field due to these lines is zero is;
Along the line between the lines closer to line#1 than line #2
Explanation:
The charges on the parallel lines #1 and #2 = Positive linear charge
The charge density on line #2, λ₂ = 2 × The charge density on line #1, λ₁
Therefore, we have;
λ₂ = 2 × λ₁
Electric field strength, E, is given as follows;
[tex]E = \dfrac{\lambda}{2\cdot \pi\cdot \epsilon_0\cdot d}[/tex]
Therefore;
[tex]E_1 = \dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}[/tex]
[tex]E_2 = \dfrac{\lambda_2}{2\cdot \pi\cdot \epsilon_0\cdot d} = 2 \times\dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}[/tex]
E₂ = 2·E₁
E₂/2 = E₁
E₂/(2·d) = E₁/d
The strength of the electric field at a given distance from line #2 is 2 times the strength of the electric field from line #1 at the same distance
Therefore the strength of the electric field will be the same at a point twice the distance from line #2 than from line #1 which is a point closer to line #1 than line #2.
