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- Homework Statement
- Attempting to determine a relationship between the height at which the magnet is dropped (relative to the centre of the solenoid) and the induced EMF in the solenoid.

- Relevant Equations
- ## \varepsilon = -N \frac{d\Phi}{dt}## ##\Phi = B A \cos \theta ##

I am currently working on an experiment that involves dropping a magnet from varying heights and measuring how the induced emf of a solenoid changes as a result. I am currently somewhat struggling with a derivation for a relationship between the two variables, however, this is what I have been thinking about so far:

- Making assumptions to make things easier: magnet maintains constant acceleration throughout the solenoid (doesnt really slow down), Magnet remains upright throughout the fall, so that theta = 0.

- The solenoid experiences the greatest magnitude of emf when it is somewhere in between one of the ends of the solenoid and the middle, where it is 0.

I have collected data, and strangely, it yielded a linear graph of emf magnitude vs. height dropped.

Here is also a graph of what one trial of dropping the magnet at 0cm above the top of solenoid (5.4cm above the centre) looks like (emf vs. time)

Thanks for any help!

- Making assumptions to make things easier: magnet maintains constant acceleration throughout the solenoid (doesnt really slow down), Magnet remains upright throughout the fall, so that theta = 0.

- The solenoid experiences the greatest magnitude of emf when it is somewhere in between one of the ends of the solenoid and the middle, where it is 0.

I have collected data, and strangely, it yielded a linear graph of emf magnitude vs. height dropped.

Here is also a graph of what one trial of dropping the magnet at 0cm above the top of solenoid (5.4cm above the centre) looks like (emf vs. time)

Thanks for any help!