Avery long line of charge with charge per unit length +8.00 μc/m is on the x-axis and its midpoint is at x = 0. a second very long line of charge with charge per unit length -6.00 μc/m is parallel to the x-axis at y = 11.0 cm and its midpoint is also at x = 0. at what point on the y -axis is the resultant electric field of the two lines of charge equal to zero?

at y=6.29 cm the charge of the two distribution will be equal.

Explanation:

Given:

linear charge density on the x-axis,

linear charge density of the other charge distribution,

Since both the linear charges are parallel and aligned by their centers hence we get the symmetric point along the y-axis where the electric fields will be equal.

Let the neural point be at x meters from the x-axis then the distance of that point from the y-axis will be (0.11-x) meters.

we know, the electric field due to linear charge is given as:

where:

linear charge density

r = radial distance from the center of wire

permittivity of free space

Therefore,

∴at y=6.29 cm the charge of the two distribution will be equal.