To find the induced emf in a coil, we can use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the coil. The formula for calculating the induced emf is:

emf = -N * ΔΦ/Δt

Where:
emf is the induced electromotive force,
N is the number of turns in the coil,
ΔΦ is the change in magnetic flux, and
Δt is the change in time.

In this problem, we are given the area of the coil (0.16 m2) and the change in magnetic field (from 0.1 Wb/m2 to 0.5 Wb/m2) in a time interval of 0.02 s. We need to find the induced emf.

1. Calculate the change in magnetic flux:
ΔΦ = B2 - B1
= 0.5 Wb/m2 - 0.1 Wb/m2
= 0.4 Wb/m2

2. Calculate the induced emf:
emf = -N * ΔΦ/Δt

Since we are not given the number of turns in the coil, we cannot directly calculate the emf. However, we can find the ratio of the change in magnetic flux to the change in time:

ΔΦ/Δt = (0.4 Wb/m2) / (0.02 s)
= 20 Wb/m2/s

3. Use the given area to find the number of turns in the coil:
Φ = B * A
Φ = (0.1 Wb/m2) * (0.16 m2)
Φ = 0.016 Wb

Since the magnetic flux Φ is equal to the product of the magnetic field and the area, we can rearrange the equation to solve for the magnetic field:

B = Φ / A
B = 0.016 Wb / 0.16 m2
B = 0.1 Wb/m2

4. Substitute the values into the equation for the induced emf:
emf = -N * ΔΦ/Δt
emf = -N * (0.4 Wb/m2) / (0.02 s)
emf = -20N V

Since we are only interested in the magnitude of the emf, we can drop the negative sign. Therefore, the induced emf in the coil is 20N V.

Without knowing the number of turns in the coil, we cannot determine the exact value of the induced emf. However, if we are given the value of N (which is not provided in the question), we can substitute it into the equation to find the emf.