Three particles have charges +20μC each.They are fixed at the corners of an equilateral triangle of side 0.5m .The force on each of particle has magnitude

To find the force on each particle, we can use Coulomb's Law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Since the triangle is equilateral, the distance between any two particles is the same and can be calculated using the side length of the triangle.

Let's calculate the distance between any two particles first:

The side length of the equilateral triangle is 0.5m.

The distance between any two particles in an equilateral triangle is equal to the length of one side of the triangle.

So, the distance between any two particles is 0.5m.

Now, let's calculate the force between two particles:

Using Coulomb's Law, the force (F) between two charged particles can be calculated using the formula:

F = k * (q1 * q2) / r^2

where:
- F is the force between the particles
- k is Coulomb's constant (k = 9 * 10^9 N * m^2 / C^2)
- q1 and q2 are the charges of the particles
- r is the distance between the particles

Let's plug in the values:

F = (9 * 10^9 N * m^2 / C^2) * ((+20μC) * (+20μC)) / (0.5m)^2

F = (9 * 10^9 N * m^2 / C^2) * (400μC^2) / (0.25m^2)

F = (9 * 10^9 N * m^2 / C^2) * (0.0004 C^2) / (0.25m^2)

F = (9 * 10^9 N * 0.0004 C^2) / (0.25m^2)

F = 14.4 * 10^6 N

Therefore, the force on each particle has a magnitude of 14.4 * 10^6 N.

To determine the force on each particle, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, let's assume one particle is at the origin (0, 0) and the other two particles are located at positions (0.5m, 0) and (0.25m, 0.43m) to form an equilateral triangle.

Step 1: Calculate the distance between each pair of particles:
- Distance between particle 1 and particle 2: d₁₂ = 0.5m
- Distance between particle 1 and particle 3: d₁₃ = d₂₃ = 0.5m

Step 2: Calculate the magnitude of the force between each pair of particles using Coulomb's Law:

For force between particle 1 and particle 2:
- Charge of particle 1: q₁ = +20μC = 20 * 10^(-6) C
- Charge of particle 2: q₂ = +20μC = 20 * 10^(-6) C
- Distance between particle 1 and particle 2: d₁₂ = 0.5m

Using Coulomb's Law:

F₁₂ = (k * |q₁ * q₂|) / d₁₂²

where k is the Coulomb constant, approximately 9 * 10^9 Nm²/C².

Substituting the values:

F₁₂ = (9 * 10^9 Nm²/C² * |20 * 10^(-6) C * 20 * 10^(-6) C|) / (0.5m)²

Simplifying further:

F₁₂ = (9 * 20 * 20 * 10^(-6) * 10^(-6)) / (0.5)²

Evaluate the expression:

F₁₂ ≈ 0.288 N

Forces between particle 1 and particle 3, and between particle 2 and particle 3 will have the same magnitude as the force between particle 1 and particle 2 because the charges and distances are the same.

Therefore, the magnitude of the force on each particle is approximately 0.288 N.

The force on each of particle has magnitude... no kidding.

The force will be along the directions of the sides, due to symettry.

Each of the two forces on a charge is
kqq/.5^2
but we want only the compoent in the direction of the angle bisector, which is 30 deg from each side. Therefore, net force on each corner is
2kqq/.5^2 * cos30