Electrostatic force electroscope

In summary, an electroscope is a device used to detect electric charges. A large electroscope is typically made with long wires and small spheres at the ends, with most of the charge residing on the spheres. In order to determine the total charge applied to the electroscope, the distance between the charges and the forces acting on the spheres must be taken into consideration. Using trigonometry and the equations for force and equilibrium, the total charge Q can be calculated.
  • #1
joanne
3
0
electroscope

A large electroscope is made with “leaves” that are 78-cm-long wires with tiny 24-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 3.0E1° angle with the vertical (see figure), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires.

*here is what I did...and got stuck in the middle of doing this problem*

Well, first I found the distance between Q/2 and Q/2. Then I applied this equation http://i5.photobucket.com/albums/y178/besuu4/b836e8b8cc7c00400c5910d3eca76e37.png to find Q. The problem is I don't have F (force) value to solved it by using the equation I provided. Anyway...I am just confusing myself. Hints are welcome. Thanks.
 

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  • #2
You know that the charges are not moving. This means they must be in equillibrium. Set up a free body diagram.
 
  • #3
You are told to ignore the mass of the wires. But don't ignore the mass of the charges.

Assume this occurs on Earth. (Weight a minute, is this a clue to the "missing force"?)

Can you say "trigonometry"?
 
  • #4
I think I get your clue, Chi Meson.

I know this is oscesles (sp?) triangle so the other two angle must be equal which is 60 degrees. I then used Sin(30)=X/78=39 to find the length and mutliple by 2 to get the full length (happened to be 78cm).

Then I used F=ma to find the force. F=(.024kg)(9.8m/s^2)=.2352N.
after that, I used this equation http://i5.photobucket.com/albums/y178/besuu4/b836e8b8cc7c00400c5910d3eca76e37.png to solve for Q.

.2352N=1/4*pi*8.85e-12*(Q^2/78cm^2)
So the answer is Q=1.59e-7 C, correct?
 
  • #5
so...right or not? Thanks.
 
  • #6
Not quite! The forces don't have to be equal for equilibrium as they're not in opposite directions. Also, the charge on each ball isn't Q. Inquire further for more help.
 
  • #7
joanne,

Start by identifying all the forces acting on one of the spheres. (I count three forces acting.) Label the forces in a diagram, then apply the conditions for static equilibrium: The net force must be zero. (Hint: Write two equations. One for vertical components; one for horizontal components.)
 
  • #8
Well not quite for vertical and horizontal... right? But yeah for two perpendicular directions. See if you can find out which :)
Edit: well I guess it doesn't matter, but one way you can ignore 1 of the 3 forces.
 

1. What is an electroscope?

An electroscope is a scientific instrument used to detect and measure the presence of electric charge. It consists of a metal rod with a conductive disk or ball at the top, and two thin, lightweight metal leaves attached to the bottom.

2. How does an electroscope work?

When an object with an electric charge is brought close to the electroscope, the charge will cause the leaves to either repel or attract each other, depending on the type of charge. This movement of the leaves can be observed and used to determine the presence and type of charge on the object.

3. What is electrostatic force?

Electrostatic force is the force of attraction or repulsion between two electrically charged objects. It is caused by the interaction of the electric fields surrounding the objects and is one of the four fundamental forces of nature.

4. How is electrostatic force related to an electroscope?

The electrostatic force between an object and the electroscope causes the leaves to move, indicating the presence of an electric charge. The strength of the electrostatic force can also be measured by the distance the leaves move.

5. What are some practical uses of an electroscope?

An electroscope is commonly used in physics experiments to demonstrate the principles of electrostatics. It can also be used to detect the presence of static electricity and to measure the strength of electric fields. In addition, it is used in industries such as electronics and telecommunications to test for the presence of electric charge in materials and devices.

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