# When exactly is it useful to use (electricity)

• Elbobo
In summary, there are two forms of the Coulomb constant, k and 1/(4 pi * permittivity of free space), which are both approximately equal to 9x10^9. The use of 1/(4 pi * permittivity of free space) is derived from Gauss' law and can simplify calculations involving Maxwell's equations. On the other hand, k is a constant with little physical significance by itself, but is convenient in calculations due to its singular value. Rationalizing the constant as 1/4 pi epsilon can also simplify some calculations. Ultimately, both forms are interchangeable and can be used based on personal preference or the specific problem at hand.
Elbobo
When is it more simple to use 1 / (4 pi * permitivity of free space) versus k, the Coulomb constant in electrical force/ electrical field formulas? My teacher and my textbook say there are times when it simplifies things, but I have yet to find any reasoning behind it.

They're the same thing. If you calculate it out, they're both approximately 9x10^9. The 1/(4 pi * permittivity of free space) just comes from gauss' law. Coulomb's law was developed earlier (I believe) and so in place of this, a constant was used, k, and its value experimentally calculated.

Also, without having studied gauss' law it doesn't make much sense to write it in the longer form, after all, it is just a constant.

Well that's what I thought too, but again, my teacher and my Giancoli textbook both say there are times when the calculations become simplied, somehow.

When using Maxwell's equations, you see permittivity of free space everywhere. There is no use in writing 1/(4 pi k) instead.

It seems that k is a constant with little physical significance by itself, but convenient in calculations for its singular value. Permittivity, a physical property, and Gauss's law, representing the geometry of charges, are expressed by the alternative form.

Rationalising the constant ie writing it in the form 1/4 pi epsilon makes a lot of calculations a bit simpler because for many problems the 4 pis will cancel out.Also,epsilon is a fundamental constant and it appears in the equation for the speed of light.I can only think of a few examples where the coulomb constant would be easier one of these being when calculating the force between point charges.As nabeshin pointed out they are the same thing so use whatever form you like.

## When exactly is it useful to use electricity?

1. What are the main benefits of using electricity?Electricity is a versatile and efficient form of energy that powers many modern technologies and devices, making our lives easier and more convenient. It also has a low environmental impact compared to other forms of energy, such as fossil fuels.

## What are the potential downsides of using electricity?

2. Are there any negative effects of using electricity?While electricity has many benefits, there are also some potential downsides to consider. The production of electricity can contribute to air and water pollution, and the use of electricity can be expensive for some people.

## When is electricity necessary for everyday life?

3. Can we live without using electricity?In today's modern world, it is difficult to imagine life without electricity. It is necessary for many essential tasks such as lighting, heating, cooking, and powering electronic devices. However, it is possible to live without electricity, as many people did before its widespread use.

## What are some industries that heavily rely on electricity?

4. How important is electricity for different industries?Electricity is essential for many industries, including manufacturing, transportation, healthcare, and technology. These industries rely on electricity for powering machinery, transportation vehicles, medical equipment, and electronic devices.

## How does electricity impact the environment?

5. What is the environmental impact of using electricity?The production of electricity can have negative effects on the environment, such as air and water pollution and the release of greenhouse gases. However, with the increasing use of renewable energy sources, the environmental impact of electricity is being reduced.

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