What is the magnetic flux through the solenoid

[captainjack2000]

1. Magnetic field inside a long solenoid with cross-sectional area A is given by B=(mu)nI where n is the number of turns per unit length and I is the current. Suppose that the current is given by I(t) = I(0)e^(a*t) where t is the time and a and I(0) are constants. What is the magnetic flux through the solenoid as a function of t? Hence find the induced emf outside the solenoid as a function of time

Homework Equations

Magnetic flux is the integral of B.dA
Faraday's Law: Emf = rate of change of magnetic flux through loop


Not quite sure how to start. Could someone please help!

 

[Gokul43201]

For a long solenoid, what is the direction of the B-field inside the solenoid? And is B a function of the position inside? What does this make $\int B\cdot dA~=~$ ?

 

[captainjack2000]

Inside the solenoid the magnetic field B will be horizontal. But we know from the equation B=mu*n*I that it doesn't depend on the radius of the solenoid.