Time dependence of induced emf in a loop

[JonNash]

Homework Statement

A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius R. The magnitude of the field varies with time according to B=B₀exp(-t/τ) where B₀ and τ are constants. The time dependence of the induced emf in the loop is
a) exp(-t²/τ²)
b) 1+exp(-t²/τ²)
c) 1-exp(-t/τ)
d) -exp(-t/τ)

Homework Equations

emf=-dΘ/dt
Θ=∫B.dA

The Attempt at a Solution

εdt=-dΘ
∫εdt=-∫dΘ
∫εdt=-Θ
∫εdt=-∫B.dA
∫εdt=-B∏R²
∫εdt=-B₀.exp(-t/τ)∏R²

So with this I guessed that the time dependence would be option d) -exp(-t/τ)
Is this the correct answer?

 

[TSny]

Hello, JonNash.

The question asks for the time dependence of ε. So you need to find an expression for ε as a function of time.