Coulomb force is the force of either attraction or repulsion between two charged bodies. The force is related to the magnitude and charge on the two bodies and the distance between them by Coulomb’s Law:

where

q_{1} and q_{2} is the amount of charge in Coulombs

r is the distance in meters between the charges

k is the Coulomb’s Law constant = 8.99×10^{9} N•m^{2}/C^{2}

The direction of the force depends on the positive or negative charges on the bodies. If the two charges are identical, the force is a repulsive force. If one is positive and the other negative, the force is an attractive force.

This Coulomb force example problem shows how to use this equation to find the number of electrons transferred between two bodies to generate a set amount of force over a short distance.

**Example Problem:**

Two neutrally charged bodies are separated by 1 cm. Electrons are removed from one body and placed on the second body until a force of 1×10^{-6} N is generated between them. How many electrons were transferred between the bodies?

**Solution:**

First, draw a diagram of the problem.

Define the variables:

F = coulomb force = 1×10^{-6} N

q_{1} = charge on first body

q_{2} = charge on second body

e = charge of a single electron = 1.60×10^{-19} C

k = 8.99×10^{9} N•m^{2}/C^{2}

r = distance between two bodies = 1 cm = 0.01 m

Start with the Coulomb’s Law equation.

As an electron is transferred from body 1 to body 2, body 1 becomes positive and body two becomes negative by the charge of one electron. Once the final desired force is reached, n electrons have been transferred.

q_{1} = +ne

q_{2} = -ne

The signs of the charges give the direction of the force, we are more interested in the magnitude of the force. The magnitude of the charges are identical, so we can ignore the negative sign on q_{2}. This simplifies the above equation to:

We want the number of electrons, so solve the equation for n.

Substitute in the known values. Remember to convert 1 cm to 0.01 m to keep the units consistent.

n = 6.59×10^{8}

**Answer:**

6.59×10^{8} electrons were transferred between the two bodies to produce an attractive force of 1×10^{-6} Newtons.

For another Coulomb force example problem, check out Coulomb’s Law Example Problem.

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