Balancing area of a loop and magnetic field through it

[uzair_ha91]

Question: Is it possible to change both the area of the loop and the magnetic field passing through the loop and still not have an induced emf in the loop?
Equation: change in Magnetic flux= area * magnetic flux density
My attempt: If the magnitude of magnetic field is changing, then by either increasing or decreasing the area of the loop, the change in magnetic flux associated with the loop can be kept constant. Then the induced emf will be zero.
Can you somehow prove this through the equation, numbers? Would appreciate the help.

 

[rock.freak667]

Φ=BA


Say initially you have Φ₀=B₀A₀. Then decrease B0 by 1/2 (so B₁=1/2B₀) and you increase the area by a factor of 2 (A₁=2A₀)

Φ₁=B₁A₁ =(1/2 B₀ *2A₀)=B₀A₀=Φ₀

if the changes occur in the same time interval,t, then E₀=E₁

Once there is a change in magnetic flux, there will be an emf induced. So as much as I can say, even if you decrease one and increase the other and emf is still being induced, it just has the same value as before. So the net emf induced would be zero.