# Magnetic Flux through solenoid question

1. Mar 17, 2012

### TDean2010

1. The problem statement, all variables and given/known data
"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?

2. Relevant equations

L=N$\Phi$/I

L=u0N2A/l

B-u0(N/l)I

3. 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!

2. Mar 17, 2012

### tiny-tim

Welcome to PF!

Hi TDean2010! Welcome to PF!
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! )

3. Mar 18, 2012

### 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!