Magnitude of total electrostatic force on a third particle ?

• education_24
In summary, the conversation discusses the calculation of the total electrostatic force on a third particle with a given charge and position, while taking into account the Coulomb constant and the direction of the forces. After determining the magnitude and direction of each individual force, the correct answer is obtained by subtracting the two forces, resulting in a final answer of 106.2N.
education_24

Homework Statement

A particle with charge −8 μC is located on the x-axis at the point 8 cm, and a second particle with charge −6 μC is placed on the x-axis at −6 cm.

What is the magnitude of the total electrostatic force on a third particle with charge −4 μC placed on the x-axis at −2 cm?

Homework Equations

The Coulomb constant is 9.0× 10^9 N·m2/C2.
Fe = (kq1q2/r^2)

The Attempt at a Solution

[(9*10^9)(4*10^-6)(8*10^-6)]/(0.1)^2 + [(9*10^9)(4*10^-6)(6*10^-6)]/(0.04)^2

The final answer I get is 163.8 N, which is incorrect.

Check the directions in which the forces act.

I don't understand. Does that mean I subtract the two forces?

education_24 said:
I don't understand. Does that mean I subtract the two forces?

Forces are vectors. They add as vectors. So after you've determined the magnitudes of the forces you need to determine the directions they're acting, too. "Add" them accordingly. Drawing a sketch of the scenario will help.

gneill said:
Forces are vectors. They add as vectors. So after you've determined the magnitudes of the forces you need to determine the directions they're acting, too. "Add" them accordingly. Drawing a sketch of the scenario will help.

That's exactly like I did.
Apparently it was wrong.
Please take a look at my work.

Okay, so all of the charges are negative. So between the middle (main) charge and the left charge, it wants to move right. Between the middle and the charge to the right of it, it wants to move left. The magnitude of the electrostatic force of the middle charge and the left charge is 135N. The magnitude of the electrostatic force of the middle charge and the right charge is 28.8N. Since the charge wants to go different directions in those situations, shall I subtract the two forces yielding an answer of 106.2N?

Correct.

education_24 said:
That's exactly like I did.
Apparently it was wrong.
Please take a look at my work.

I did look at your work, and one of the forces is acting in the wrong direction.

Try this. Write the calculation for each force individually and state its magnitude and direction.

EDIT: Never mind, I see you've done essentially that above. Good show

Thanks guys!

1. What is the formula for calculating the magnitude of total electrostatic force on a third particle?

The formula for calculating the magnitude of total electrostatic force on a third particle is F = k * |q1q2| / r^2, where k is the Coulomb constant, q1 and q2 are the charges of the first two particles, and r is the distance between the two particles.

2. How does the distance between two charged particles affect the magnitude of total electrostatic force on a third particle?

The magnitude of total electrostatic force on a third particle is inversely proportional to the square of the distance between two charged particles. This means that as the distance between the two particles increases, the magnitude of the force on the third particle decreases.

3. Can the magnitude of total electrostatic force on a third particle ever be negative?

No, the magnitude of total electrostatic force on a third particle can never be negative. It is always a positive value, as the force between two charged particles is always attractive or repulsive but never both at the same time.

4. How does the magnitude of the charges of two particles affect the magnitude of total electrostatic force on a third particle?

The greater the magnitude of the charges of two particles, the greater the magnitude of total electrostatic force on a third particle will be. This is because the force is directly proportional to the product of the two charges.

5. What is the unit of measurement for the magnitude of total electrostatic force on a third particle?

The unit for the magnitude of total electrostatic force on a third particle is Newtons (N), as it is a measure of force.

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