# Electric Forces: Solve for Distance Below

• BunDa4Th
In summary, the conversation discusses the problem of finding the distance between two electrons where the electrostatic force exerted by one cancels out the gravitational force on the other. The solution involves setting the equations for gravitational force and electrostatic force equal to each other and solving for the distance. The variables used include the masses of the electron and Earth, as well as the charge of an electron.

## Homework Statement

An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. How far below the first electron is the second? M

## Homework Equations

F = G(MeMp)/r^2
F = Ke|q1||q2|/r^2

## The Attempt at a Solution

I am not sure how to attempt this problem but this is what i thought.

F = (6.67 x 10^-11) (9.11 x 10^-31)(1.67 x 10^-27)/r^2

my problem there is i don't know how to find F to solve for r. its the same way if i use the other formula I still don't know F to solve for r.

I don't understand this at all and what numbers am i suppose to find to do this.

All you have to do for this is make the gravitational force equal to the electrostatic force and solve for r. That is:

$$G\frac{M_Em_e}{r_e^2}=K\frac{e^2}{r^2}$$

Remember re is the radius of the Earth and r is the distance between the electrons so they are not the same thing if that's what was confusing you originally.

Okay, I understand the formula a bit but not sure of what the varibles are.

M_E = mass of electron?
m_e = mass of earth?
e = ?

e is the charge on an electron.

Thanks for the help on solving this.

I have one question, How did you get the equation K(e^2/r^2)?

BunDa4Th said:
Thanks for the help on solving this.

I have one question, How did you get the equation K(e^2/r^2)?

Since e is the charge of the electron and your system has two electrons, it is shorter to write K(e^2/r^2) rather than K(e*e/r^2).

Okay, I get it now thanks for the explanation.

## 1. How is the distance between two electric charges calculated?

The distance between two electric charges is calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 2. What is the unit of measurement for electric force?

The unit of measurement for electric force is the Newton (N), which is the same unit used for measuring other types of force.

## 3. How do you solve for the distance between two electric charges?

To solve for the distance between two electric charges, you can rearrange Coulomb's law to solve for the distance (r) by dividing the force (F) by the product of the charges (q1 and q2) and taking the square root of the result: r = √(k * q1 * q2 / F), where k is the constant for Coulomb's law.

## 4. Can the distance between two electric charges ever be negative?

No, the distance between two electric charges cannot be negative. Distance is a positive quantity and is always measured as the absolute value between two points.

## 5. How do the magnitude and direction of electric force change as the distance between two charges changes?

The magnitude of electric force decreases as the distance between two charges increases, following the inverse square law. The direction of electric force is always along the line connecting the two charges, and it remains the same regardless of the distance between them.