Force between two charged particles at a distance question, help please?

In summary: Just remember to include the units in your calculations. So for the last line it should be:q=√(0.0288 m^2 x 1N) / 9x10^9 N*m^2/C^2q=1.78 x 10^-6 C
  • #1
kirsten_2009
137
2

Homework Statement



Two small electrically charged objects are placed 6 centimeters (cm) apart, where they exert a force of 8 N on each other. How far apart must they be placed in order to exert a force of 1 N on each other? Assuming that the charges on the two objects are equal, what is the charge?

Homework Equations



F = q1 x q2 / d^2

The Attempt at a Solution



This questions seems to be simple to me, yet, I don't know why I'm so stuck...so...here is my reasoning:

If at 6 cm, the force = 8N and we want to find out what the distance between the charged particles is when the force between them is 1N...I'm assuming that they would have to be further apart so the force between them decreases by a magnitude of 8 times...and since the force weakens as the distance between the particles is squared then: square root of 8 = 2.82 x 6 cm = 16.97 cm? (I'm not sure if that is correct) and then to find the charge on the particles...I'm at a loss...but assume that if the above calculation is correct; I could substitute the values into the equation and clear for q^2? Thanks in advance for any help you can give me!
 
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  • #2
kirsten_2009 said:
F = q1 x q2 / d^2
Don't forget the constant k (Coulomb's constant).

kirsten_2009 said:
If at 6 cm, the force = 8N and we want to find out what the distance between the charged particles is when the force between them is 1N...I'm assuming that they would have to be further apart so the force between them decreases by a magnitude of 8 times...and since the force weakens as the distance between the particles is squared then: square root of 8 = 2.82 x 6 cm = 16.97 cm? (I'm not sure if that is correct)
Good!

kirsten_2009 said:
and then to find the charge on the particles...I'm at a loss...but assume that if the above calculation is correct; I could substitute the values into the equation and clear for q^2?
This problem has nothing really to do with the first part. Just pick one of the distances, plug the given data into Coulomb's law, and solve for the charge. Careful with units! And don't forget that constant.
 
  • #3
Hello Doc Al,

Thanks for your reply and help...so...would this be correct?

F=9x10^9 * q1 x q2 / d^2
1N=9x10^9 * q^2 / 0.1697m^2
q=√0.0288m x 1N / 9x10^9
q=1.78 x 10^-6 Coulombs

Thanks so much!
 
  • #4
kirsten_2009 said:
Hello Doc Al,

Thanks for your reply and help...so...would this be correct?

F=9x10^9 * q1 x q2 / d^2
1N=9x10^9 * q^2 / 0.1697m^2
q=√0.0288m x 1N / 9x10^9
q=1.78 x 10^-6 Coulombs

Looks good!
 
  • #5


Your reasoning is correct. To find the distance at which the force is 1N, we can use the equation F = q1 x q2 / d^2 and rearrange it to solve for d: d = √(q1 x q2 / F). Plugging in the values, we get d = √(q1 x q2 / 1N) = √(q1 x q2) = 2.82 x 6 cm = 16.97 cm.

To find the charge on the particles, we can use the same equation and solve for q1 or q2. Since the charges on the two particles are equal, we can set q1 = q2 = q and solve for q: q = √(F x d^2) = √(1N x 16.97 cm^2) = 4.12 x 10^-5 C.

Therefore, the charges on the two particles are both 4.12 x 10^-5 C and they must be placed 16.97 cm apart to exert a force of 1N on each other.
 

1. What is the force between two charged particles at a distance?

The force between two charged particles at a distance is known as the Coulomb force and is given by Coulomb's Law. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

2. How do you calculate the force between two charged particles at a distance?

To calculate the force between two charged particles, you can use the formula F = k(q1*q2)/r^2, where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles in Coulombs, and r is the distance between them in meters.

3. What is the unit of force between two charged particles at a distance?

The unit of force between two charged particles is Newtons (N) in the SI system of units. In the CGS system, the unit of force is dynes (dyn).

4. How does the force between two charged particles change with distance?

The force between two charged particles is inversely proportional to the square of the distance between them. This means that as the distance between the particles increases, the force decreases. Conversely, as the distance decreases, the force increases.

5. What factors affect the force between two charged particles at a distance?

The force between two charged particles is affected by the magnitude of the charges, the distance between them, and the medium or material in which the particles are located. The medium can affect the force through its dielectric constant, which is a measure of how well it can insulate or polarize in response to an electric field.

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