Question

Two charged particles are fixed to the x-axis: particle 1 of charge q₁ = 20µC at x = 0.2m, and particle 2 of charge q₂ = −80µC at x = 0.8m. At what coordinate along the x-axis is the net electric field produced by the particles equal to zero?

Answer 1

To find the coordinate along the x-axis where the net electric field produced by the particles is zero, we use the superposition principle and calculate the net electric field using the individual electric fields produced by each particle. By setting the equation for the net electric field equal to zero, we can solve for the coordinate.

Step-by-step explanation:

To find the coordinate along the x-axis where the net electric field produced by the particles is equal to zero, we need to consider the superposition principle. According to this principle, the total electric field at any point is the vector sum of the electric fields produced by each charged particle individually.

Let's denote the distance from the first particle (q₁) to the point where the net electric field is zero as r₁ and the distance from the second particle (q₂) to the same point as r₂. The net electric field at this point can be calculated using the formula:

E_net = (k * q₁) / r₁² + (k * q₂) / r₂²

By setting this equation equal to zero, we can solve for r₁ and r₂. Let's denote the coordinate we are looking for as x. We can express r₁ and r₂ in terms of x:

r₁ = x - 0.2

r₂ = 0.8 - x

Substituting these expressions into the equation for the net electric field, we get:

(k * q₁) / (x - 0.2)² + (k * q₂) / (0.8 - x)² = 0

Solving this equation will give us the coordinate along the x-axis where the net electric field is zero.