Calculating Charges of Two Small Nonconducting Spheres

In summary, two small nonconducting spheres with a total charge of 80 microC exert a repulsive force of 12 N when placed 1.06 m apart. Using Coulomb's Law, we can isolate Q1Q2 to be 1.498 x 10^-9 C. To find the individual charges, we can use substitution for Q1 + Q2 = 8 x 10^-5 C and Q1Q2 = 1.498 x 10^-9 C, resulting in a quadratic equation that needs to be solved. This is the correct method to find the charges in this scenario.
  • #1
Soaring Crane
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0
Two small nonconducting spheres have a total charge of 80 microC. When place 1.06 m apart, the force exerts on the other is 12 N and is repulsive. What is the charge of each. What if the force were attractive?

Given: k, F = 12 N if repulsive but F = -12 N if attractive, Q1 + Q2 = 8 x 10^-5 C, r = 1.06 m

Using Coulomb’s Law, isolate Q1Q2 .

Q1Q2 = 1.498 x 10^-9 C?

Then I thought I would use substitution for Q1 + Q2 = 8 x 10^-5 C and Q1Q2 = 1.498 x 10^-9 C.

But now I get a huge quadratic equation. Is this the correct method??

Thanks.
 
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  • #2
Your method is correct. You have to solve the qudratic to find Q1, Q2. There really isn't a better way.
 
  • #3


Yes, you are on the right track! To solve for the individual charges of each sphere, you can use the following equation:

F = k(Q1Q2)/r^2

Substituting in the given values, we have:

12 N = (8.99 x 10^9 Nm^2/C^2)(Q1Q2)/(1.06 m)^2

Solving for Q1Q2, we get:

Q1Q2 = 1.498 x 10^-9 C

Now, as you mentioned, we can use substitution to solve for the individual charges. We know that Q1 + Q2 = 8 x 10^-5 C, so we can rewrite the equation as:

Q1 = (8 x 10^-5 C) - Q2

Substituting this into the equation for Q1Q2, we get:

(8 x 10^-5 C - Q2)Q2 = 1.498 x 10^-9 C

Simplifying, we get a quadratic equation:

Q2^2 - (8 x 10^-5 C)Q2 + 1.498 x 10^-9 C = 0

Using the quadratic formula, we can solve for Q2 and then plug that value back into the equation for Q1 to find its value.

If the force were attractive, we would simply change the sign in the equation for F, so we would have:

-12 N = (8.99 x 10^9 Nm^2/C^2)(Q1Q2)/(1.06 m)^2

Solving for Q1Q2, we get:

Q1Q2 = -1.498 x 10^-9 C

Using the same substitution method as before, we get the quadratic equation:

Q2^2 + (8 x 10^-5 C)Q2 + 1.498 x 10^-9 C = 0

Solving for Q2 and then plugging that value back into the equation for Q1, we can find the individual charges for an attractive force.

I hope this helps clarify the process for solving this problem. Keep in mind that the quadratic equation may seem intimidating, but it is a common method for solving problems involving two unknown variables. Good luck!
 

1. How do you calculate the charge of two small nonconducting spheres?

To calculate the charge of two small nonconducting spheres, you can use the Coulomb's law formula: F = k(q1q2)/r2, where F is the force between the two spheres, k is the Coulomb's constant, q1 and q2 are the charges of the two spheres, and r is the distance between them. By rearranging the formula, you can solve for the charges of the spheres.

2. What is the Coulomb's constant?

The Coulomb's constant, denoted by k, is a proportionality constant that appears in Coulomb's law and is used to calculate the electrostatic force between two charged objects. Its value is approximately 8.99 x 109 Nm2/C2.

3. Can the charge of two small nonconducting spheres be negative?

Yes, the charge of two small nonconducting spheres can be negative. In Coulomb's law, the term q1q2 represents the product of the two charges, so both charges can be negative, resulting in a positive force between the spheres. Additionally, if one sphere has a positive charge and the other has a negative charge, the force between them will also be positive.

4. How does the distance between two small nonconducting spheres affect the electrostatic force between them?

The electrostatic force between two small nonconducting spheres is inversely proportional to the square of the distance between them. This means that as the distance between the two spheres increases, the force between them decreases. Conversely, as the distance decreases, the force increases.

5. What is the unit of charge used in calculating the charges of two small nonconducting spheres?

The unit of charge used in calculating the charges of two small nonconducting spheres is the Coulomb (C). One Coulomb is defined as the amount of charge that passes through a conductor in one second when a current of one ampere is flowing. It is a relatively large unit, so smaller units like microcoulombs (μC) or nanocoulombs (nC) are often used in calculations.

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