- #1

- 30

- 0

## 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=B

_{0}exp(-t/τ) where B

_{0}and τ are constants. The time dependence of the induced emf in the loop is

a) exp(-t

^{2}/τ

^{2})

b) 1+exp(-t

^{2}/τ

^{2})

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∏R

^{2}

∫εdt=-B

_{0}.exp(-t/τ)∏R

^{2}

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

Is this the correct answer?