How Does Loop Size Affect Magnetic Flux in a Solenoid Setup?

[spriter]

Homework Statement

A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1350 turns per meter and a diameter of 5.55 cm, and carries a current of 2.20A

Homework Equations

Magnetic Field (B) of a solenoid: B = $$\mu_{0}$$*(N/L)*I
Where $$\mu_{0} = 4pi * 10^{-7} T*m/A$$ , N/L is loops per unit length, and I is current

$$\Phi = B*A*Cos\theta$$

The Attempt at a Solution

I tried doing this: I use the Magnetic Field of a solenoid formula to find the magnetic field through the solenoid - because I know the magnetic field within the axis of the solenoid is constant, I thought I could just find the value of that constant B and then find the flux using the other formula for the different values of L (area) - and for areas larger than the circle of the solenoid - I could take the area of the flux as the area of the circle.

However, when I put my answer in, it tells me that the answer must be expressed in terms of L (I don't know if that's supposed to be the side length of the square or if it's supposed to be the length of the solenoid).Thanks.

 

[rl.bhat]

Take the area of the loop as L^2 and find the flux through it.

 

[spriter]

Oh, sorry: I forgot a bit of information:

There are three parts to the question:

A) Find the magnetic flux through the loop when L = 2.35 cm.

B) Find the magnetic flux through the loop when L = 5.55×10−2 cm

C) Find the magnetic flux through the loop when L = 12.5 cm

That's what I was getting confused about, since it gives you L - why is it asking you to put it in terms of L - or does it mean put it in terms of the length of the solenoid?

Thanks