Find ∆V while sliding a card through a card reader with magnetic field

[kayneblue12]

Homework Statement

You can slide your (old style, magnetic strip) credit card in a reader, and it somehow gets your credit card number. How does it do this?, Explain, with appropriate equations, what voltage ∆V you will see (as a function of time) if you slide the strip – with its magnetized regions – past a reader coil of wire as shown above.

Relevant Equations

motional emf = vBL, emf = dΦ/dt

emf = dΦ/dt = (B*A)*d/dt = B(dA/dt), dA/dt= L*d/dt(vt) = L*v, emf = B*L*v per coil

Since there are 25 loops the total emf= 25(vBL) This is where I'm am stuck. Would I assume that B is 24 uT, the velocity as 3m/s , and the length as 1mm? If so I would get ∆V as 1.8*10^-6.

 

[BvU]

Hello Kayne, $\quad$ $\quad$ !

Sound reasoning. I think you have the right amplitude. But the exercise asks 'what voltage ∆V you will see'
So can you describe what the signal looks like ? (e.g. 'it's a sine wave')

 

[TSny]

and the length as 1mm

There are several lengths depicted in the diagram. Which one should be used for L?

 

[BvU]

I think you have the right amplitude

In view of @TSny 's post: reconsider !
Question: how does it look? still open

 

[collinsmark]

@kayneblue12,

In case you haven't figured this out yet, you should consider your calculations at several different scenarios.

What's the voltage when a magnetized region is in the process of entering the coil's area?

What's the voltage when a magnetized region is in the process of leaving the coil's area?

Also, according to your diagram, some magnetic regions have the magnetic field $B = 24 \ \mathrm{\mu T}$ while others have $B = 25 \ \mathrm{\mu T}$. I'm not sure if that's a mistake or not, but you shouldn't ignore it unless you are given a correction.