# Magnetic Flux through solenoid question

• TDean2010
In summary, the conversation discusses calculating the magnetic flux through a solenoid with 400 turns and a magnetic field of 1.5mT at the center. The correct calculation is found by multiplying the magnetic field by the area, rather than using the equations given.
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!

Welcome to PF!

Hi TDean2010! Welcome to PF!
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?

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! )

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!

## 1. What is magnetic flux through a solenoid?

Magnetic flux through a solenoid refers to the measure of the total magnetic field passing through the surface of a solenoid. It is a measure of the strength of the magnetic field lines passing through the solenoid.

## 2. How is magnetic flux through a solenoid calculated?

Magnetic flux through a solenoid is calculated by multiplying the strength of the magnetic field (B) by the cross-sectional area of the solenoid (A) and the cosine of the angle between the magnetic field and the surface of the solenoid (θ). The formula is Φ = B x A x cos(θ).

## 3. What factors affect the magnetic flux through a solenoid?

The factors that affect the magnetic flux through a solenoid include the strength of the magnetic field, the number of turns in the solenoid, the cross-sectional area of the solenoid, and the material of the solenoid. Any changes in these factors will impact the magnetic flux through the solenoid.

## 4. How does changing the number of turns in a solenoid affect the magnetic flux?

Changing the number of turns in a solenoid will directly affect the magnetic flux. Increasing the number of turns will increase the magnetic flux, while decreasing the number of turns will decrease the magnetic flux. This is because more turns will result in a stronger magnetic field passing through the solenoid.

## 5. Can the magnetic flux through a solenoid be negative?

Yes, the magnetic flux through a solenoid can be negative. This occurs when the angle between the magnetic field and the surface of the solenoid is greater than 90 degrees. In this case, the cosine of the angle will be negative, resulting in a negative magnetic flux value.

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