ELS - Electric Force and Coulomb's Law

Electric Force and Couloumb's Law

Introduction

We've seen how like electrical charges will repel each other while opposite charges will attract. The strength of that force is given by Coulomb's Law:

Where r is the distance between the charges and each Q represents the charge of an object. Electric charge is measured in SI units of coulombs (C). The term k is a proportionality constant that equals 8.988 x 10⁹ N•m²/C². (This can easily be rounded to 9.0 x 10⁹). It is important to note that this equation only gives the magnitude of the force between two charged objects, so positive and negative charges mean nothing in the equation. The direction will always be along a line that runs between the two points. Each charge will experience the same force, but in an opposite direction. This is in accordance with Newton's 3^rd Law. If the charges are of like sign, they will each experience force F pointed directly away from the other charge. If they are of opposite sign the force will be directed towards the other charge.

A note on charges: Since an object's charge is based on its number of electrons versus protons, the charge must always be a discrete multiple of the charge of an electron/proton. This base charge is called the elementary (or fundamental) charge. e = 1.602 x 10^-19 C. An electron will have a charge of -e while a proton's charge is ±e. According to Coulombs Law, if two 1 C charges were placed 1 m apart, they would experience a force of 9 x 10⁹ N repelling them. We tend to deal with charges significantly less than 1 C. You'll often see units of micro-coulombs (μC = 1 x 10^-6 C) or nano-coulombs (nC = 1 x 10^-9 C). For this reason you want to make sure you are up to speed on your metric prefixes.

The proportionality constant k is often written in terms of another constant, ε₀, called the permittivity of free space.

Coulomb's Law Practice #1

Determine the magnitude and direction of the electric force on the electron of a hydrogen atom exerted by the proton in the atom's nucleus. Assume the average distance between the revolving electron and the proton is. 

Click here for the solution to the practice problem. Links to an external site.

Watch the presentation below to see how to handle solving Coulomb's Law problems when several charges are involved.

 

Coulomb's Law Practice #2

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