Question

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is
along a line between the lines closer to line #2 than line #1.


at a point midway between the lines.


along a line between the lines closer to line #1 than line #2.


along a line perpendicular to lines #1 and #2.

Answer 1

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;

$E = \dfrac{\lambda}{2\cdot \pi\cdot \epsilon_0\cdot d}$

Therefore;

$E_1 = \dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}$

$E_2 = \dfrac{\lambda_2}{2\cdot \pi\cdot \epsilon_0\cdot d} = 2 \times\dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}$

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.