Application of Coloumb's Law to electroscope

In summary, the problem deals with a large electroscope with two 75-cm wires and 22g balls at the ends, where all the charge resides on the balls. The wires make a 30 degree angle with the vertical and the total charge Q applied to the electroscope needs to be determined. To find this, Coulomb's Law is used and the system is observed to be in static equilibrium. The downward force of gravity is resolved horizontally to equal the charge force, which is opposed by the tension in the leaves.
  • #1
Theelectricchild
260
0
Hi there, I am having a bit of difficulty with this problem dealing with a little more difficult application of Couloumbs Law.

A large electroscope has two wires that are 75-cm long w/22g balls at the ends. When charged, all the charge resides on the balls (Q/2 for each ball) If the wires each make a 30 degree angle with the vertical, what total charge Q must have been applied to the electroscope?

So I set up my free body diagrams and I know how to figure out the weight force and i believe i can get tension--- but what should I be doing to know how much force electrical force is applied (Repulsion in this case since both charges are positive) to make that 30 degree angle to the vertical?

I need to be thinking back to mechanics a little bit =P

Any help would be appreciated--- thank you.
 
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  • #2
but what should I be doing to know how much force electrical force is applied

Use Coulomb's Law. Also observe the system is in static equilibrium.
 
  • #3
yes net force is = to 0 because a = 0. Thank you I noticed that actually right after i posted this--- silly me.
 
  • #4
Down ward force = mg applied to each side this must be resolved horizontally to equal the charge force which opposes it -- a little trigonometry.
 
  • #5
There is no horizontal component of a downward force.
 
  • #6
John not directly your right , but the leaves are held apart by a horizontal force and they are trying to fall due to a vertical force , obviously something connects these two.
 
  • #7
It isn't the force of gravity, but rather the tension in the leaves, that has the horizontal force component that opposes the charge force.
 

1. How does Coloumb's Law apply to an electroscope?

Coloumb's Law 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. In an electroscope, this law applies to the repulsion between the charged particles in the metal leaves, causing them to move apart.

2. What factors affect the deflection of an electroscope?

The deflection of an electroscope is affected by the charge of the particles, the distance between them, and the material of the electroscope. The force between the charged particles increases with increasing charge and decreases with increasing distance. Additionally, different materials have different levels of conductivity, which can affect the movement of the particles.

3. How can Coloumb's Law be used to determine the charge on an electroscope?

To determine the charge on an electroscope, Coloumb's Law can be used to calculate the force between the charged particles in the metal leaves. By measuring the distance between the leaves and the amount of deflection, the charge on the electroscope can be calculated.

4. Can Coloumb's Law be used to explain the behavior of an electroscope when different objects are brought near it?

Yes, Coloumb's Law can be used to explain the behavior of an electroscope when different objects are brought near it. When a charged object is brought near the electroscope, the force of attraction or repulsion between the charged particles in the electroscope and the charged object will cause the leaves to either collapse or repel, respectively.

5. What are some real-world applications of Coloumb's Law to electroscope?

Coloumb's Law is used in many real-world applications, such as in the design of electronic devices, the study of electricity and magnetism, and in the development of technologies like Van de Graaff generators and electrostatic precipitators. It is also used in the field of forensic science to analyze evidence in cases involving electrocution or electrostatic discharge.

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