Magnetic Flux through solenoid question

[TDean2010]

Homework Statement

"A solenoid is wound with 400 turns on a form 4cm in diameter and 50 cm long. The windings carry a current that produces a magnetic field, of magnitude 1.5mT, at the center of the solenoid. The magnetic flux through the solenoid is closest to?

Homework Equations

L=N\Phi/I

L=u₀N²A/l

B-u₀(N/l)I

The Attempt at a Solution

So I calculated the current and inductance using the last 2 equations, getting I=1.492A and L = 5.05x10^-4
Then plugging that stuff into the self inductance equation and solving for magnetic flux I got 1.9x10^-6 Txm^2. But the answer my teacher gave in the solution key was 7.5x10^-4 Txm^2. I understand the difference between these two answers is having N=400 or not dividing by N at all when solving for magnetic flux, but I don't get why. I thought it would be 7.5x10^-4 if he had been asking for the flux in one turn (N=1), not the whole thing.

Is there something I am not reading in the question correctly that is making me think \Phi = LI/N and using N=400 is correct? That is, can someone explain to me why the answer is 7.5x10^-4 snf noy 1.9x106-6?

Thank you very much!

 

[tiny-tim]

Welcome to PF!

Hi TDean2010! Welcome to PF!

"A solenoid is wound with 400 turns on a form 4cm in diameter and 50 cm long. The windings carry a current that produces a magnetic field, of magnitude 1.5mT, at the center of the solenoid. The magnetic flux through the solenoid is closest to?

Why are you going into all that detail?

Learn your electric units … tesla = webers per square metre (T = Wb m^-2) …

the magnetic flux through an area is simply the magnetic field times the area!

(assuming the magnetic field is constant … otherwise, messy integration! )

 

[TDean2010]

Thank you! I definitely need to work on my units and I need to stop over complicating things. After calculating it again I got the correct answer. Thanks for the help!