How Does Mutual Induction Depend on Current Changes Over Time?

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The discussion centers on the calculation of mutual induction using the formula for electromotive force (emf) in relation to current changes over time. The specific formula used is \(\epsilon = -M \frac{I(0.8) - I(0)}{0.8 - 0}\), where \(\epsilon = -3.2\). A critical point raised is the necessity of using the derivative of current rather than assuming a linear change, as indicated by the more complex current function provided in the referenced image. The correct approach requires acknowledging the non-linear nature of current changes over time.

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http://i28.tinypic.com/ot42gi.jpg

in normal induction finding question
we need to have how a current changes over some period
of time

and emf.

but here i don't have that
i only have emf =-3.2
in t=0.8 i can find a certain current
and in t=0 i can find a certain current.(using the given formula )
i can put them in the formula and get M
[tex] \epsilon=-M\frac{I(0.8)-I(0)}{0.8-0}[/tex]
is it ok??

because they presented a much more complicated current.
 
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Sorry, but yours doesn't work. The answer shown in the jpg is the correct way. You have assumed with your equation that the change in current with time is linear instead of using the more complicated form that was given. You need to take the derivative as indicated.
 

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