- #1

rugerts

- 153

- 11

## 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 Φ

*B*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.