# The Physics Problem Solver/Electromagnetism/Electric Charge and Coulomb's Law

The scalar form of Coulomb's law is an expression for the magnitude and sign of the electrostatic force between two idealized *point charges*, small in size compared to their separation. This force (*F*) acting simultaneously on point charges (*q*_{1}) and (*q*_{2}), is given by

where *r* is the separation distance and *k*_{e} is a proportionality constant. A positive force implies it is repulsive, while a negative force implies it is attractive. The proportionality constant *k*_{e}, called the **Coulomb constant** (sometimes called the **Coulomb force constant**), is related to defined and can be calculated based on knowledge of empirical measurements of the speed of light:

## Exercises[edit]

### Beginner[edit]

1) Two point charges are initially 9 cm apart and are then moved so they are 2 cm apart. If the initial force between them is F what is the new force in terms of the initial force?

- Using

For the initial state, r = 9cm = 0.09m

For the initial state, r = 2cm = 0.02m

Multiplying by r^{2} in both cases gives us:

Setting the two equations to be equal ( they are both equal to ):

**Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle F_{f}={\frac {0.09^{2}}{0.02^{2}}}\times F_{i}=20.25F_{i}\,}**

In other words, the new force is roughly 20x as strong as the initial force.