Integration Problem: Solving Compact Results in Electrodynamics

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In summary, the conversation is about solving a specific integration, with a given equation and constants, mentioned in the context of electrodynamics and referenced to two textbooks. The speaker is seeking help and clarification on how to solve the integration in a more compact way.
  • #1
Psi-String
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Hi! Could someone give me an idea how the following integration be carried out??

[tex] \int \frac{r dr}{ \left( r^2 + a^2 - 2rau \right)^{3/2}} = \frac{ru - a}{a(1-u^2)\sqrt{r^2 + a^2 - 2rau}} [/tex]

where u and a are constant.

I have encounter such integration several times in electrodynamics.

I can solve it in lengthy way, but can't carry out such compact result as above. Could someone help me?? Thanks a lot!
 
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  • #2
Look up Sadikus textbook. Or David Griffiths. You'll find a good result there.
 
  • #3
well, this is an integration I need to carry out when solving Griffiths' problem. The solution manual only give the result as above, it didn't take out step by step, and I don't think it is that obvious that we can solve it just by one equation XDDDD
 

FAQ: Integration Problem: Solving Compact Results in Electrodynamics

What is the importance of solving compact results in electrodynamics?

The compact results in electrodynamics, also known as the compact equations, are a set of simplified equations that describe the behavior of electromagnetic fields. These equations are crucial for understanding and predicting the behavior of electric and magnetic fields in various systems, such as circuits and antennas.

What is the process of solving compact results in electrodynamics?

The process of solving compact results in electrodynamics involves using mathematical techniques, such as vector calculus and differential equations, to manipulate the equations and find solutions for specific scenarios. This often involves simplifying the equations, applying boundary conditions, and solving for the unknown variables.

What are some common applications of compact results in electrodynamics?

The compact equations are used in a wide range of applications, including designing and analyzing electronic circuits and devices, understanding the behavior of electromagnetic waves in communication systems, and predicting the behavior of antennas and radar systems.

What are the challenges of solving compact results in electrodynamics?

One of the main challenges of solving compact results in electrodynamics is the complexity of the equations and the need for advanced mathematical skills. Another challenge is the need to carefully consider and apply boundary conditions, which can significantly affect the solutions.

What are some resources for learning how to solve compact results in electrodynamics?

There are many resources available for learning how to solve compact results in electrodynamics, including textbooks, online courses, and tutorials. It is also helpful to have a strong foundation in vector calculus, differential equations, and electromagnetics. Additionally, working with a mentor or joining a study group can provide valuable support and guidance.

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