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Solenoid, EMF and flux

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1. Homework Statement
In Solenoid, is emf E= N. d(phi)/dt, or is it simply d(phi)/dt? Some books contain the latter one. It was not a big deal until i gave a thought about it. Since increasing the N, we are actually increasing the value of n, thus increasing B= (mu) .n.I
So, by placing N in front of the differential, are not we considering the same thing twice?
2. Homework Equations


3. The Attempt at a Solution
 

Merlin3189

Homework Helper
Gold Member
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Have a look at, for example, Hyperphysics article on inductance.

Yes you are using the number of turns twice (I'm not sure what N and n are) for exactly the reason you say: the flux depends on the number of turns and the emf depends on the number of turns x rate of change of flux, so inductance is proportional to turns2.
 

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