# Coulomb's Law problem: Charged particles and the net electric field and force

• lydia_y620
In summary: Please clarify.I am not sure what you are referring to. Can you please provide more context or information?
lydia_y620

## Homework Statement

Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 19e. Particle 3 of charge q3 = +16e is initially on the x axis near particle 2.Then particle 3 is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3 changes. Figure (b) gives the x component of that net force as a function of the position x of particle 3. The scale of the x axis is set by xs = 1.70 m. The plot has an asymptote of F2,net = 0.8688 × 10-25 N as x → ∞. As a multiple of e and including the sign, what is the charge q2 of particle 2?

F = kq1q2/r2

## The Attempt at a Solution

As x --> ∞, the force on particle 2 comes just from particle 1, so the force from particle 1 is always 0.8688 x 10^-25 N because particles 1 and 2 are stationary.
When x = 0.85 for particle 3, the net force on particle 2 is 0, so the force from particle 1 must equal the force from particle 3.
This means that 0.8688 x 10^-25 = k(q2*16e)/0.85^2
Is this correct? Apparently my answer is incorrect after I tried solving for q2 in terms of e.

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lydia_y620 said:
1. Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 19e. Particle 3 of charge q3 = +16e is initially on the x axis near particle 2.Then particle 3 is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3 changes. Figure (b) gives the x component of that net force as a function of the position x of particle 3. The scale of the x axis is set by xs = 1.70 m. The plot has an asymptote of F2,net = 0.8688 × 10-25 N as x → ∞. As a multiple of e and including the sign, what is the charge q2 of particle 2?
View attachment 112319

F = kq1q2/r2

## The Attempt at a Solution

As x --> ∞, the force on particle 2 comes just from particle 1, so the force from particle 1 is always 0.8688 x 10^-25 N because particles 1 and 2 are stationary.
When x = 0.85 for particle 3, the net force on particle 2 is 0, so the force from particle 1 must equal the force from particle 3.
This means that 0.8688 x 10^-25 = k(q2*16e)/0.85^2
Is this correct? Apparently my answer is incorrect after I tried solving for q2 in terms of e.[/B]
I note that it asks for the charge as a multiple of e, but your last equation would naturally give a multiple of 1/e.

haruspex said:
I note that it asks for the charge as a multiple of e, but your last equation would naturally give a multiple of 1/e.
My final answer was (4.359 x 10^-37)/e, which, like you've said, doesn't make sense because it's a multiple of 1/e.

lydia_y620 said:
My final answer was (4.359 x 10^-37)/e, which, like you've said, doesn't make sense because it's a multiple of 1/e.
It does make sense. It arises naturally from q1=Fr2/(kq2).
So express it as constant x e instead. e is a known value.

The checker is not taking it as that.

NSchool2000 said:
The checker is not taking it as that.
What checker is not taking what as what?

## 1. What is Coulomb's Law and how is it used to solve problems involving charged particles?

Coulomb's Law is a fundamental law in electrostatics that describes the relationship between the electrostatic force, the charge of two particles, and the distance between them. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is used to calculate the electric field and force between charged particles in a given system.

## 2. How do you determine the net electric field and force in a system of charged particles?

To determine the net electric field, you first need to calculate the individual electric fields of each charged particle using Coulomb's Law. Then, you can use vector addition to find the resultant electric field. To determine the net electric force, you can use the same process, but instead of calculating electric fields, you calculate the individual forces between each pair of charged particles and then use vector addition to find the resultant force.

## 3. Can Coulomb's Law be used for both positive and negative charges?

Yes, Coulomb's Law can be used for both positive and negative charges. The force between two like charges (both positive or both negative) is repulsive, while the force between two unlike charges (one positive and one negative) is attractive. The only difference is that the direction of the force will be opposite for like charges and unlike charges.

## 4. What is the significance of the constant k in Coulomb's Law?

The constant k in Coulomb's Law is known as the Coulomb's constant and has a value of 8.99 x 10^9 Nm^2/C^2. This constant is used to account for the permittivity of free space and ensures that the units of the electric field and force are in Newtons per Coulomb. It also allows for easier comparison between different systems with varying charges and distances.

## 5. Are there any limitations to using Coulomb's Law?

Coulomb's Law is only valid for stationary charges and does not take into account the effects of relativity. It also assumes that the charges are point charges, meaning they have no size or shape. Additionally, Coulomb's Law only applies to electrostatic situations and does not account for the effects of moving charges or magnetic fields.

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