Charge on two suspended metal balls

In summary, two metal coated foam spheres with masses of 2.80x10^-6kg are attached to nylon threads 45cm long and hung from a common point. When given equal quantities of negative charge, each thread makes a 15 degree angle with the vertical. Using the equations F=(kQ1Q2)/r^2 and F=ma, the charge on each sphere can be found to be 6.66x10^-9, which is significantly different from the initial estimate of 1.8x10^-9 due to rounding errors and incorrect assumptions about the triangle formed by the threads. The solution involves drawing a free-body diagram and resolving forces along the x and y directions.
  • #1
crowdedscience
6
0

Homework Statement


Two very small metal coated foam spheres, each of mass 2.80x10^-6kg, are attached to nylon threads 45cm long and hung from a common point. When the spheres are given equal quantities of negative charge, each supporting thread makes an angle of 15 degrees with the vertical. Find the charge on each sphere.


Homework Equations


F=(kQ1Q2)/r^2 in the form of Q=√((Fr^2)/k) as Q1 and Q2 will be the same.
F=ma
probably Pythagoras and sine/tangent/cosine ratios


The Attempt at a Solution


ok, so r or the distance between the charges was pretty obvious. If the strings are 0.45m long and the angle at the point where the strings combine is 30° (2x15°), then its going to be an equilateral triangle so r=0.45m (I think). I suppose we are assuming k=9X10^9. Noe for the force. The force of gravity will be 2.80x10^-6x9.8 (F=ma), which equals approximately 2.7x10^-7. I then did (2.7x10^-7)/tan(90-15), which equals about 7.4x10^-8. I thought that equaled half the force of repulsion of the sphere, but I'm not sure. If that's right then the total force of repulsion is 1.5x10^-7. So then
Q=√((1.5X10^-7x0.45^2)/9x10^9). That equaled 1.8X10^-9. But the actual answer is 6.66X10^-9. I know my rounding is having quite and effect on it, so i did it again, using as many decimals as I could but I was still quite a bit off. What am I doing wrong?
 
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  • #2
An equilateral triangle has angles of 60° - this one has a top angle of 30°.
 
  • #3
oh wow, oopsies!
 
  • #4
I don't really understand your solution attempt here.
Start by drawing a free-body diagram for one of the charges and resolve the forces along the x and y directions.
You should be able to eliminate the tension leaving only 1 unknown ( the charge ).
 
  • #5
crowdedscience said:

Homework Statement


... angle at the point where the strings combine is 30° (2x15°), then its going to be an equilateral triangle so r=0.45m
First and foremost, when did you learn that an equilateral triangle has an angle 30°? It's not an equilateral triangle!
This one will be isosceles!
Next why are you taking the weight as it is? Take its horizontal components!
Then I don't get why you are dividing by tan75°. Could you explain that?
 
  • #6
Rookie mistake. You are unworthy of this forum. Next time go to yahoo answers...
 

1. What is the concept behind charge on two suspended metal balls?

The concept behind charge on two suspended metal balls is based on the principles of electrostatics. When two metal balls are suspended close to each other, they can acquire a net charge due to the transfer of electrons between them. This charge can either be positive or negative depending on the relative charge of the metal balls.

2. How do the metal balls acquire a charge?

The metal balls can acquire a charge through the process of induction. When a charged object is brought close to the metal balls, the electrons in the metal balls will be repelled or attracted, causing a redistribution of charge. This results in one metal ball having a positive charge and the other having a negative charge.

3. What factors affect the amount of charge on the metal balls?

The amount of charge on the metal balls is affected by several factors such as the distance between the balls, the material and size of the balls, and the relative charge of the objects interacting with the balls. The charge on the balls will also decrease over time due to the dissipation of charge through the air.

4. How can the charge on the metal balls be measured?

The charge on the metal balls can be measured using an electroscope, which is a device that detects the presence and magnitude of electric charge. The electroscope works by using a metal rod to transfer the charge from the balls to a metal plate, which then causes a deflection of a gold leaf or needle, indicating the presence of charge.

5. What are the practical applications of the charge on two suspended metal balls?

The charge on two suspended metal balls has several practical applications, such as in electrostatic generators, which use the transfer of charge between two metal balls to create an electric current. This concept is also used in electrostatic precipitators to remove pollutants from industrial exhaust gases. Additionally, the charge on metal balls can be used in experiments to demonstrate the principles of electrostatics and charge induction.

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