Powering an LED via Induced Current

[rugerts]

Homework Statement

As the title suggests, I have a school project where I’m supposed to design a hand shake flashlight using AWG 34 copper wire, a niobium cylindrical magnet, hard paper (sort of like cardboard), and a red LED. The goal’s to get the red LED to light.

My teacher gave some hints in that the cross sectional area will be constant and that the only thing really varying will be the magnetic field.

So, by Faraday’s law of induction, the induced EMF in the generator depends on the number of loops, the change in magnetic field, the change in cross sectional area and the rate at which they change.

So far, I know a few things since I've been given them.
Strength of the magnet is around 1.3 T
the wire's Resistance per meter can be found on Wikipedia since it's AWG
the dimensions of the magnet are 0.004 m radius and 0.015 m height
LED requires at least 1.4 V to light up

Homework Equations

where E is the electromotive force (EMF) and ΦB is the magnetic flux.
Ohm's Law may be useful as well.

The Attempt at a Solution

In order to do this, it seems as though I’ve got to somehow estimate the magnetic field term by looking at the number of shakes I can do in a given time interval.

I need to make estimations for the number of turns in my wire. I believe that as the coils get thicker, this will have some effect on my results. I'm not entirely sure why, but believe it has something to do with resistance.

I've been trying to use Faraday's law, and since I was told the area will be fixed (but that the wire's thickness can affect this fixed area) I just used the radius of the magnet for the cross sectional area of the tube (so it's a tight fit). We've been told the delta T value is indirectly related to the frequency of shakes I can produce. The delta B is sort of tripping me up. I'm not sure how to go about this. I know that I need to find the conditions that'll give me the largest change in magnetic field through the tube.

Originally, I had thought that the cylindrical magnet would actually not be wrapped around a cylindrical paper tube, and that the magnet would be turned perpendicular, since from my reading of the textbook I saw that generators produce max induced EMF when area vector and B field lines are perpendicular since the change is occurring rapidly as the flux goes to zero. However, I no longer think that's the case because: 1) all designs of regular shake flashlights don't incorporate this and 2) the situation with the generator is different since the armature is spinning. In my case, the magnetic field is moving, and the area would be in place.

Can anyone please point me in the right direction or offer any insights?
Thank you for your time.

 

[berkeman]

I think it will be hard to calculate much here from first principles, unfortunately. Do you have the magnet and some wire already? It may be useful to try some experiments to start to box in this problem.

The moving magnet in a cylindrical coil is an inferior generator, unfortunately. Something more like a conventional rotating generator configuration us much more efficient. Can you comment on why that is?

If you are limited to the inefficient linear shaker configuration, your next task will be to try to figure out what the best number of coils is to try to optimize this. You are constrained on what gauge of wire to use, right? How many turns of wire will give you a few Ohms of resistance? Why is that important?

 

[berkeman]

I have a school project where I’m supposed to design a hand shake flashlight using AWG 34 copper wire, a niobium cylindrical magnet, hard paper (sort of like cardboard), and a red LED. The goal’s to get the red LED to light.

My teacher gave some hints

BTW, there is a serious flaw in the materials list that you have been given. There are other small flaws, like the lack of a storage capacitor, but there is something else that is missing from the design specification that can cause some potential designs to blow up the LED. Do you have any thoughts about what that issue may be? Be sure to read through typical LED datasheets to look for the clues about this...

 

[rugerts]

I think it will be hard to calculate much here from first principles, unfortunately. Do you have the magnet and some wire already? It may be useful to try some experiments to start to box in this problem.

The moving magnet in a cylindrical coil is an inferior generator, unfortunately. Something more like a conventional rotating generator configuration us much more efficient. Can you comment on why that is?

If you are limited to the inefficient linear shaker configuration, your next task will be to try to figure out what the best number of coils is to try to optimize this. You are constrained on what gauge of wire to use, right? How many turns of wire will give you a few Ohms of resistance? Why is that important?

Yes, unfortunately I'm limited to the linear shaker for now.
Yeah, I guess there's quite a few things flawed in the experiment, but I don't get to make up the rules here so I'll make do with what I'm given.

The resistance will play an important role here so that I don't blow out the LED like you said. But, it can't be too high, otherwise the LED won't light, correct? I believe I'll be using Faraday's Law to find the number of turns, N, the coil should have.

 

[berkeman]

The resistance will play an important role here so that I don't blow out the LED like you said.

The resistance won't be important in preventing the LED failure. It's important as part of maximizing the power transfer to the LED.

I believe I'll be using Faraday's Law to find the number of turns, N, the coil should have.

The problem with that is you don't know the flux from the magnet very well. You may be able to estimate it, though. Show us your initial calcs and we can comment on them.

 

[rugerts]

The resistance won't be important in preventing the LED failure. It's important as part of maximizing the power transfer to the LED.

The problem with that is you don't know the flux from the magnet very well. You may be able to estimate it, though. Show us your initial calcs and we can comment on them.

https://imgur.com/a/YZMmnIq
So, I'm a little stuck here. I can't see how the resistance comes into play, or how I might solve for this magnetic field. Any tips?

 

[SammyS]

https://imgur.com/a/YZMmnIq
So, I'm a little stuck here. I can't see how the resistance comes into play, or how I might solve for this magnetic field. Any tips?

If you're going to post an Image, it's best to use the UPLOAD feature.

.

 

[rugerts]

If you're going to post an Image, it's best to use the UPLOAD feature.
View attachment 233830
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Sorry, thank you.

 

[rugerts]

Nevermind y’all. I managed to make it work! I was pretty excited. Thanks anyways

 

[berkeman]

Nevermind y’all. I managed to make it work! I was pretty excited. Thanks anyways

Congrats!

And to help you learn more about LEDs, the answer to my question about potential damage to the LED was regarding the Max Reverse Voltage that can be tolerated by the LED. From a typical datasheet:

https://www.mouser.com/ds/2/239/LTST-S326KGKFKT-1143909.pdf

 

[rugerts]

https://imgur.com/a/YZMmnIq
So, I'm a little stuck here. I can't see how the resistance comes into play, or how I might solve for this magnetic field. Any tips?

Congrats!

And to help you learn more about LEDs, the answer to my question about potential damage to the LED was regarding the Max Reverse Voltage that can be tolerated by the LED. From a typical datasheet:

https://www.mouser.com/ds/2/239/LTST-S326KGKFKT-1143909.pdf

View attachment 233879

Thanks. So, I found my number of turns by good deal of estimating and using Faraday's Law. I was wondering if there's a way I can do this using calculus. Namely, if I take iR(N) = N (dphi/dt), Where R is the resistance as a function of the number of turns N. Then differentiate the equation with respect to N. Then set di/dN = 0 to find the maximum. It seems like it should work, but I'm having trouble actually working out the math. Any tips?