# A little problem on dimensional analysis

• jeremy22511
In summary, the conversation discusses the dimensions of energy and how they can be derived using the fundamental dimensions of time, length, and mass. The question is raised whether the dimensions of p.d. and coulomb can be simplified using these fundamental dimensions, and it is concluded that they are already the simplest.
jeremy22511

## Homework Statement

The dimensions for all sorts of energy must be equal.
Then the following should hold:
By E=Fs and E=VIt,
[Fs] = [VIt]
[M][L]2[T]-2=[V][Q]

Now, according to some online lectures I watched some time ago, the dimensions of time, length, and mass are the three fundamental dimensions and all other dimensions can be derived with the three. So I was wondering if I could simplify the dimension of the p.d. and the coulomb into the three dimensions.

Would appreciate any help. Thanks.
Jeremy

## The Attempt at a Solution

I asked my high school teacher the other day and he said that the dimensions for the coulomb and p.d. are already the simplest...

In an electric field F = E*Q
And V = E*d
Therefore Energy = V*Q = E*d*F/E = F*d.

Oh. I didn't realize it was that simple. Thanks.

## 1. What is dimensional analysis and why is it important in science?

Dimensional analysis is a mathematical method used to convert units of measurement and ensure that calculations are accurate. It is important in science because it helps to maintain consistency and avoid errors in calculations that involve different units of measurement.

## 2. How is dimensional analysis used in scientific experiments?

Dimensional analysis is commonly used in scientific experiments to convert measurements into different units and to ensure that all measurements are consistent. It is also used to check the validity of equations and to determine whether experimental data supports a specific hypothesis.

## 3. Can dimensional analysis be applied to all types of measurements?

Yes, dimensional analysis can be applied to all types of measurements, including length, mass, time, temperature, volume, and more. It is a universal method that can be used in all areas of science and engineering.

## 4. How does dimensional analysis help to solve problems in real-world situations?

Dimensional analysis can help to solve problems in real-world situations by providing a systematic approach to converting units of measurement. It can also help to identify and correct errors in calculations, making it a valuable tool in many scientific and engineering fields.

## 5. Are there any limitations to dimensional analysis?

While dimensional analysis is a useful tool, it does have its limitations. It cannot account for certain variables that may affect measurements, such as human error or changes in environmental conditions. It also cannot be used to convert between units that are not related by a common physical quantity.

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