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A level physics- Further mechanics question (1)

can someone explain to me the link between these two formulas :
>𝑁Ф = 𝐵AN cos 𝜃
>emf induced in a rotating coil 𝜀 = 𝐵ANwsin (𝜔 t)

-someone told me you just differentiate the first one to get the 2nd one which I can see but why is that ?
(edited 3 months ago)
Original post by 1234kelly
can someone explain to me the link between these two formulas :
>𝑁Ф = 𝐵AN cos 𝜃
>emf induced in a rotating coil 𝜀 = 𝐵ANwsin (𝜔 t)

-someone told me you just differentiate the first one to get the 2nd one which I can see but why is that ?

Have you studied Faraday's law of electromagnetic induction?

Faraday's law of electromagnetic induction states the following:
The emf ε induced is the negative change in the magnetic flux linkage Φm per unit time.
Since the magnetic flux linkage is 𝐵AN cos (𝜔 t) , then the change in the magnetic flux linkage Φm per unit time is just differentiating the magnetic flux linkage Φm with respect to time.

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