Determining charge of q and the spring coated with metal?

In summary, two uncharged metal spheres, 1 and 2, are connected by an insulating spring with a spring constant of 30.0 N/m. When charges of +q and -q are placed on the spheres, the spring contracts to a length of 1.250 m. Using the formula Fs = kΔx, the charge q is calculated to be 3.96e-05 C. For a conducting spring, the length would change to 1.55 m.
  • #1
Richard Ros
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Homework Statement


Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating spring (unstretched length L0 = 1.55 m, spring constant k = 30.0 N/m), as shown in the figure.
Charges +q and –q are then placed on the spheres, and the spring contracts to length L = 1.250 m. Recall that the force exerted by a spring is Fs = kΔx, where Δx is the change in the spring's length from its equilibrium length. {Correct Answer: a. 3.96e-05 C, b. 1.55 m}

(a) Determine the charge q. (b) If the spring is coated with metal to make it conducting, what is the new length of the spring?

Homework Equations



1/4πε0 * q1*q2/r^2
f = -kΔx

The Attempt at a Solution


I set fe = fs and got my answer for letter a as 3.16*10^-5 C, which is incorrect from the actual answer. Not sure why it's .8 difference in value. For letter b, I have no idea how to do b.
 

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  • #2
Your method for a is correct, you just forgot to write the 1/r².

For question b, you just need to think about what happens to the charges. What changes when you go from an insulated spring to a conducting one?
 
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1. How do you determine the charge of a q and a spring coated with metal?

To determine the charge of a q and a spring coated with metal, you can use a device called an electroscope. Place the metal-coated spring on the electroscope and bring a charged object close to it. The electroscope will show a deflection, and by measuring the angle of deflection, you can determine the charge of the spring and q.

2. Can the charge of a q and a spring coated with metal be negative?

Yes, the charge of a q and a spring coated with metal can be negative. The electroscope will show a deflection in the opposite direction if the charge is negative.

3. How does the metal coating on the spring affect its charge?

The metal coating on the spring acts as a conductor, allowing the charge to distribute evenly along the spring. This results in a more accurate measurement of the charge compared to an uncoated spring.

4. Is it possible to determine the charge of a q and a spring coated with metal without an electroscope?

Yes, it is possible to determine the charge of a q and a spring coated with metal without an electroscope. One method is to use a known charge and measure the force of repulsion or attraction between the charged object and the spring. Another method is to use a charge sensor, which can detect the charge without direct contact.

5. How can the charge of a q and a spring coated with metal be used in scientific experiments?

The charge of a q and a spring coated with metal can be used in various scientific experiments, such as studying the behavior of electric fields, testing the properties of conductors and insulators, and investigating the relationship between charge and force. It is also commonly used in electrostatic demonstrations and experiments in physics classrooms.

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