How Do You Calculate the Total Charge in a Solenoid with Time-varying EMF?

[latitude]

Homework Statement

A selfinduced emf in a solenoid of inductance L changes in time as E = E.e^-kt. Find the total charge that passes through the solenoid, assuming the charge is finite.

Homework Equations

E = LdI/dt
U = 1/2LI^2
I = dQ/dt

The Attempt at a Solution

I'm pretty stumped by this one, honestly. I thought I might have to use I(t) = E/R(1 - e^-Rt/L) somehow. I don't really understand how the emf is changing in time?

 

[rock.freak667]

Homework Statement

A selfinduced emf in a solenoid of inductance L changes in time as E = E.e^-kt. Find the total charge that passes through the solenoid, assuming the charge is finite.

The Attempt at a Solution

I'm pretty stumped by this one, honestly. I thought I might have to use I(t) = E/R(1 - e^-Rt/L) somehow. I don't really understand how the emf is changing in time?

Well I am not sure if the Es in E=E.e^-kt are the same but you can do this

L(dI/dt)=Ee^-kt and then do something similar with dQ/dt