# What Is the Magnetic Flux through a Loop in a Solenoid?

• tnbstudent
In summary, a wire circle with a radius of 0.050 m is embedded in a solenoid with a length of 0.20 m and 1000 turns carrying a current of 0.50 A. Using the formula for magnetic field in a solenoid and the formula for flux, the magnetic flux through the loop can be calculated to be approximately 3.1 x 10^-5 T*m^2. However, it is important to note that a more accurate solution would require a flux integral, which is not covered in this section.
tnbstudent

## Homework Statement

A wire circle of radius 0.050 m is embedded in a solenoid of length 0.20 m with 1000 turns that carries a current of 0.50 A. If a vector that is normal to the plane of the circle makes a 40° angle with the axis of the solenoid, what is the magnetic flux through the loop?

## Homework Equations

B (solenoid) = μ*I*n
Flux = B*A*cosθ

## The Attempt at a Solution

n=1000/.2
I'm using the loops per unit length
l=.20m
r=0.05m
I=0.5A
I plugged in the values to solve for the magnetic field:
B=(4*∏*10^-7)*(0.5A)*(1000/.2)
B=0.031T

A=(∏r^2)*(l)
A=1.5e-4 m^3

I'm having some trouble visualizing the angle, but I think the angle should be 50?

Can someone point me in the right direction?

Plugged in? You have to do a flux integral.
the flux If the solenoid points alon an axis, z, the angle between the magnetic field and the circle is still 40deg. So
$\Phi = \int \vec{B}_{solenoid}\cdot d\vec{a} = \int |B_{solenoid}|\cos(\theta) da =|B_{solenoid}|\int \cos(\theta)da$
B goes out in front because it is constant over the circle. So do the surface integral yourself.
I would always suggest to do the solution algebraically first, then insert numbers, and then evaluate your result. Is it realistic and does it diverge at any point.
And always draw your situation, saves a lot of trouble.

Thanks - I'm sure you are correct, but we will not get to integrals until a later section. I would like to get the answer using the tools from this section which are the formulas I listed above.
Thanks again - I should have been more specific with my question.

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

Magnetic flux through a solenoid is the measure of the total magnetic field passing through the solenoid. It is represented by the symbol Φ (phi) and is measured in units of webers (Wb).

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

The magnetic flux through a solenoid can be calculated by multiplying the number of turns in the solenoid (N) by the current flowing through it (I) and the area of the cross-section of the solenoid (A). This can be represented by the formula Φ = NIA.

## 3. What is the relationship between the magnetic field and the magnetic flux through a solenoid?

The magnetic field inside a solenoid is directly proportional to the magnetic flux passing through it. This means that as the magnetic field increases, the magnetic flux also increases.

## 4. How does the length of a solenoid affect the magnetic flux through it?

The length of a solenoid does not have a direct effect on the magnetic flux passing through it. However, a longer solenoid will have a larger cross-sectional area and therefore can accommodate more turns, resulting in a larger magnetic flux.

## 5. What factors can change the magnetic flux through a solenoid?

The magnetic flux through a solenoid can be changed by varying the current flowing through it, changing the number of turns in the solenoid, or altering the cross-sectional area of the solenoid. Additionally, the presence of a magnetic material inside the solenoid can also affect the magnetic flux passing through it.

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