Magnetic Flux through solenoid question

AI Thread Summary
The discussion revolves around calculating the magnetic flux through a solenoid with 400 turns, a diameter of 4 cm, and a length of 50 cm, producing a magnetic field of 1.5 mT. The initial calculations led to a magnetic flux of 1.9x10^-6 Txm^2, which differed from the teacher's answer of 7.5x10^-4 Txm^2. The confusion stemmed from the use of the number of turns (N) in the magnetic flux formula. It was clarified that the magnetic flux should be calculated using the magnetic field multiplied by the cross-sectional area of the solenoid, without dividing by N. Ultimately, the correct approach simplified the calculation, leading to the accurate answer.
TDean2010
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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!
 
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Welcome to PF!

Hi TDean2010! Welcome to PF! :smile:
TDean2010 said:
"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? :confused:

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! :smile:

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

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