Flux through loop around solenoid

[gboff21]

Homework Statement

A simple loop of 5 cm radius encompasses the middle turns of a long coil. The coil has 2500-turns,
is of length 1 m and radius 1 cm, and carries a current of 10 Amps. What is the magnetic flux through the single loop?

Homework Equations

B=μIN/L with L=1: B=μIN
flux=∫B.dA

The Attempt at a Solution

flux= μIN*A(loop)= 4π*10^-7*10*π*(5*10^-2)^2
This is not right apparently

the actual answer uses the area of the solenoid. Why is that? FLux is the B field dotted with perpendicular area, so why is it the solenoid area? That means that flux is independent of the loop's size!

 

[truesearch]

That is correct.
Flux DENSITY = B = Webers/m^2
Flux is in Webers = B x A.
The solenoid is what is producing the flux and it is constant = B x Area of solenoid

 

[gboff21]

But I'm looking for the flux through the loop!

 

[tiny-tim]

truesearch is right …

there's no magnetic field (and no flux) outside the solenoid ​

 

[gboff21]

But the question asks if there is a magnetic flux through the loop which is outside the solenoid!