Total induced emf at different speeds

[cryptoguy]

Homework Statement

Suppose you have a coil that is a certain distance from a magnet. Now you move the coil towards the magnet (until it is on top of the magnet) at a certain speed. Then you do the same thing only faster. Will the total induced emf be the same for both tries? Aka should the integrals of the two V_induced vs t plots be the same magnitude, opposite sign?

Homework Equations

Faraday's...

The Attempt at a Solution

I'm not at all sure... I'm doing a lab on this and be got different values for the total induced emf, but I have a hunch that it should be the same, can't really explain it though.
Thanks for any hints.

 

[Hootenanny]

Faraday's law basically states that the induced emf is equal to the rate of change of the magnetic flux with respect to time. Now, if you move the magnetic through the coil faster, does the rate of change of magnetic flux with respect to time remain unchanged, increase or decrease?

 

[cryptoguy]

if you move it faster... sounds like it'll increase

 

[Hootenanny]

if you move it faster... sounds like it'll increase

Correct! So what would happen to the induced emf?

 

[cryptoguy]

it would... also increase? Yet if you move the coil faster towards the magnet, the instantaneous induced emf does increase, but the total time of movement decreases.