Apositive point charge q1 = 2.5 x 10-5 c is fixed at the origin of coordinates, and a negative point charge q2 = -5.0 x 10-6 c is fixed to the x axis at x = +2.0 m. find the location of the place(s) along the x axis where the electric field due to these two charges is zero.

3.62 m  and - 1.4 m

Explanation:

Consider a location towards the positive side of x-axis beyond the location of charge Q₂

x = distance of the location from charge Q₂

d = distance between the two charges = 2 m

For the electric field to be zero at the location

E₁ = Electric field by charge Q₁ at the location = E₂ = Electric field by charge Q₂ at the location

x = 1.62 m

So location is 2 + 1.62 = 3.62 m

Consider a location towards the negative side of x-axis beyond the location of charge Q₁

x = distance of the location from charge Q₁

d = distance between the two charges = 2 m

For the electric field to be zero at the location

E₁ = Electric field by charge Q₁ at the location = E₂ = Electric field by charge Q₂ at the location

x = - 1.4 m

a is the best answer your welcome