Faraday's Law in the frequency domain

I'm trying to figure out what faraday's law is in terms of frequency rather than time.

I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.

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You can generate a Faraday induction voltage by either an oscillating magnetic field

B(t) = B0 sin(ωt)

or an oscillating area

A(t) =A0 sin(ωt)

An example of the latter is a conductor loop rotating in a dc magnetic field.

So V(t) = -NAωB0 cos(ωt) or -NBωA0 cos(ωt)

Here, ω = 2πf

Bob S

I am trying to determine the oscilating magnetic field. In that equation what is t? Is that the period over which i am sampling the antenna?

I am trying to determine the oscilating magnetic field. In that equation what is t? Is that the period over which i am sampling the antenna?

B(t) = B0 sin(ωt)

So V(t) = -NAωB0 cos(ωt)

Where ω = 2πf and t is time. The output voltage is an oscillating voltage, just like the magnetic field.

Bob S

That makes so much sense! Thanks