# Calculating how many surplus electrons on each sphere

• hotram
In summary, two identical 9.60-g metal spheres are hung from separate 500-mm strings and surplus electrons are added to each sphere. When brought into contact, the spheres reach equilibrium with each string making a 15.0 ∘ angle with the vertical. The number of surplus electrons on each sphere can be determined by converting all numbers to SI units, finding the distance between the two balls, and using Coulomb's Law to calculate the charge on each ball.
hotram

## Homework Statement

Two identical 9.60-g metal spheres (small enough to be treated as particles) are hung from separate 500-mm strings attached to the same nail in a ceiling. Surplus electrons are added to each sphere, and then the spheres are brought into contact with each other and released. Their equilibrium position is such that each string makes a 15.0 ∘ angle with the vertical

How many surplus electrons are on each sphere?

## Homework Equations

9.6g=.0096kg
500mm=.5m
F(elec.)=k(Q1)(Q2)/(r^2)
e= -1.602*10^(-19)

## The Attempt at a Solution

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I first began by converting all numbers to SI units

Then I found the distance between the 2 balls (not sure)
d=.5sin(15)

charge, I was not sure how to get this to use coulomb so I took the total mass .0096kg/(1.7*10^(-27))= an N

N/2= number of electrons in each ball

And I got lost here.

I do not know how to find charge of objects in this scenario. All I know is they are the same charge because there are repelling

hotram said:
each string makes a 15.0 ∘ angle with the vertical
hotram said:
d=.5sin(15)
Each is at 15 degrees to the vertical. Draw the diagram, and mark the forces acting.

## 1. How do you calculate the number of surplus electrons on each sphere?

To calculate the number of surplus electrons on each sphere, you need to first determine the net charge on each sphere. This can be done by subtracting the number of protons from the number of electrons on each sphere. The difference will give you the net charge, which can then be converted to the number of surplus electrons.

## 2. What factors affect the number of surplus electrons on each sphere?

The number of surplus electrons on each sphere is affected by the material of the spheres, the distance between them, and the presence of any external forces or fields. Different materials have different tendencies to gain or lose electrons, and the distance between the spheres affects the strength of the electric force between them.

## 3. Can the number of surplus electrons on each sphere be negative?

Yes, the number of surplus electrons on each sphere can be negative. This means that the sphere has a net positive charge, indicating a deficit of electrons. This can happen if the sphere loses some of its electrons through contact with another material or due to external forces.

## 4. How does the number of surplus electrons on each sphere affect the electric force between them?

The number of surplus electrons on each sphere directly affects the electric force between them. The greater the difference in the number of surplus electrons, the stronger the electric force will be. This can result in stronger attractions or repulsions between the spheres.

## 5. How can the number of surplus electrons on each sphere be determined experimentally?

The number of surplus electrons on each sphere can be determined experimentally by using a device such as an electroscope or a Faraday cage. These devices can measure the net charge on each sphere and from there, the number of surplus electrons can be calculated. Alternatively, the spheres can be subjected to different conditions and their net charge can be measured before and after to determine the impact on the number of surplus electrons.

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