Two particles are located on the x axis of a cartesian coordinate system particle 1 carries a charge of 3.0 nc and is at x 40 mm and particle 2 carries a charge of 3.0 nc and is at x 40 mm particle 3 which carries a charge of 9.0 μc is located on the positive y axis 90 mm from the origin what is the magnitude of the vector sum of the electric forces exerted on particle 3?

what is the direction angle of the vector sum of the electric forces exerted on particle 3 measured counterclockwise from the positive x axis?

F = 45.6  N

, θ = 90

Explanation:

The electric force is given by Coulomb's law

             F = k q₁ q₂ / r₁₂²

Where k is the Coulomb constant that you are worth 8.99 10⁹ N m²/C², q are the charges and r is the distance between them

The easiest way to solve this problem is to find the force on each axis, the two particles on the x-axis have the same charge and are one at x = 40 mm and the other at x = -40mm,

X axis

         Fₓ = F₁₃ₓ - F₂₃ₓ = 0

Axis y

        = +

The modulus of this force is the same

        Fy = 2

Let's reduce the magnitudes to the SI system

        q₁ = 3.0 nC = 3.0 10⁻⁹ C

        x₁ = 40 mm = 0.040 m

        q₂ = 3.0 10⁻⁹ C

        x₂ = -0.040 m

        q₃ = 9.0 10⁻⁹ C

        y₃ = 0.090 m

Let's look for the electric force

          = k q₁ q₃ / r₁₃²

         r₁₃ = √ ((0.04-0)² + (0-0.09)²)

         r₁₃ = 0.09849 m

          = 8.99 10⁹ 3 10⁻⁶  9 10⁻⁶ / 0.09849

          = 2.552 10¹  N = 25.52 N

To find the component of this force we will use trigonometry

         tan θ = y / x

         θ = tan⁻¹ 90/40

         θ = 66⁰

Now we can find the vertical components of this force

          sin 66 = /

          = sin66

          = 25.52 sin66

          = 22.8  N

The total vertical force is

             = 2 22.8

            =  45.6 N

We can find the magnitude of the total force using the Pythagorean theorem

           F² = Fₓ² +  ²

           F² =   ²

           F = 45.6  N

     The angle can be found using trigonometry

         Tan θ =    / Fₓ

         θ = 90