Understanding a Homopolar Generator

In summary, the conversation involves a discussion about a homopolar generator and its proposed solution. The speaker is struggling to understand the derivation of ##dl## and its purpose in the solution. Another person explains that ##dl## represents the position vector along the path of integration and suggests using ##\vec{l}## instead to avoid confusion.
  • #1
jisbon
476
30
Homework Statement
Give an expression for the induced current in a homopolar generator as a function of angular velocity ##\omega##
Relevant Equations
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So I was searching up on the homopolar generator and found this explanation for the generator, as well as the proposed solution.

1569639604738.png


1569639629066.png


However, I don't really understand what the solution is trying to do here.

Ok, I understand to find the current, you will need the potential, which is the integration of emf. However, I'm stuck at the last part. How did they exactly derive ##dl ##and what is ##dl## exactly?

Any explanation will be appreciated. Thanks
 
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  • #2
Hi.
##d\mathbf{l}## is along the line between shaft and contact point. ##d\mathbf{l}## and emf working on the line have same direction, with plus or minus signature.
 
  • #3
I think the integral "overloads" the symbol ##r## as it uses it both at the integral boundary (from 0 to r) and to denote the position vector along the path of integration which is along a radius R. I think it would be more proper to denote the ##\vec{r}## as ##\vec{l}## and then everything falls into place cause then ##d\vec{l}## gains its meaning inside the integral.
 

FAQ: Understanding a Homopolar Generator

What is a homopolar generator?

A homopolar generator is a type of electrical generator that produces direct current (DC) by using a magnetic field and a rotating conductive disk.

How does a homopolar generator work?

A homopolar generator works by using the principle of electromagnetic induction. As the conductive disk rotates, it cuts through the magnetic field, creating a current flow in the disk. This current is then collected by brushes or contacts and can be used as a source of electricity.

What are the advantages of a homopolar generator?

One advantage of a homopolar generator is its simplicity. It has fewer moving parts compared to other types of generators, making it more reliable and easier to maintain. It also produces a continuous and stable output of direct current.

What are the applications of a homopolar generator?

Homopolar generators are commonly used in high-power applications where a continuous and stable source of direct current is required. They are often used in large-scale industrial processes, such as aluminum smelting and electroplating. They can also be used in experimental physics research to produce intense magnetic fields.

Are there any limitations to a homopolar generator?

One limitation of a homopolar generator is that it can only produce relatively low voltages. Therefore, it is not suitable for applications that require high voltages. Additionally, the conductive disk can experience a significant amount of wear and tear due to the constant rotation, which may require frequent maintenance or replacement.

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