Calculate Induced EMF in Circular Loop: Cylindrical Coordinates

[TOUHID11]

TL;DR Summary

How can I express the induced EMF in terms of the radius of the loop, through a uniform yet changing B field, in order to calculate the curl of the induced electric field?

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore its curl. So in terms of cylindrical coordinate system, the 𝑠̂ , 𝜙̂ cancel out and with respect to electric field the 𝐸𝑠 and 𝐸𝑧 is simply zero. So we are left with the curl of the electric field in the 𝑧̂ direction and the electric field in the 𝐸𝜙. And we ultimately end up with:
∇×𝐸⃗ =𝑧̂ [1/𝑟 ∂/∂𝑟 (𝑉𝑖𝑛𝑑𝑢𝑐𝑒𝑑/2𝜋𝑟)]
So here, how do I write the 𝑉𝑖𝑛𝑑𝑢𝑐𝑒𝑑 in terms of s, to calculate for the partial "s" derivative, and therefore calculate the magnitude of the curl. If there's any conceptual or calculation errors, please do suggest where I have gone wrong.

 

[Babadag]

The magnetic flux has to be the product of B and the projection of the loop area on a surface perpendicular to B. α=2*pi()*s*t

 

[Babadag]

Sorry. I forgot to mention:
Emf=-dφ/dt ; φ=B*pi()*r^2*cos(2*pi()*s*t)^2 ;s=speed [rps]
I=Emf/Zloop
E[electric field]=ρ*J [current density];ρ=loop resistivity.
J=I/loop cross section area.

 

[Babadag]

Correction:

Let's say the loop rotates about a diameter with s rotations per second[rps].

Then the loop projection area will be п*r^2*cos(α)

α=2*п *s*t and the magnetic flux will be:

φ=B*п*r^2*cos(2*п*s*t)

*=multiply by [x] as in Microsoft excel