Flux in a Uniform Magnetic Field

In summary, the conversation discusses induced emf and magnetic flux, specifically points 3 and 4 which are in contradiction with each other. The misunderstanding is clarified by considering the wire as a container of conduction electrons and the forces acting on them in a magnetic field. The misunderstanding lies in the bounds of each term in the equation Φ=B⋅A, with A being the surface area of the conductor. As the wire moves through the space, the value of A for that specific space changes, resulting in a change in flux and an induced emf.
  • #1
Cardinalmont
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Thank you for reading my post. I was thinking about induced emf and magnetic flux and I realized I have a huge misunderstanding, but I don't know exactly what it is. Below I will list 4 statements which I logically know cannot all be simultaneously true. Can you please tell me which one(s) are incorrect in order to aid my understanding?

1. In order to create an emf in a conductor there must be a change in magnetic flux.
This can be seen by ε=NΔΦ/Δt, If ΔΦ=0 then so will ε

2. Magnetic flux is equal to the product of a conductor's surface area, magnetic field passing through that surface area, and the angle between the two. This is given by Φ=B⋅A

3 When a wire moves through a uniform magnetic field, neither its surface area, nor the strength of the magnetic field, nor the angle between the two are changing ∴ change in magnetic flux = 0 ∴ There is no induced emf.

4 When a wire moves through a uniform magnetic field, an electromagnetic force will force electrons in the wire to one side inducing an emf.

It is clear to see that points 3 and 4 are in direct contradiction of each other. I believe 3 is false, but I can't see the logical flaw! Please help me!

Thank you.
 

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  • #2
Number 3 is incorrect because the wire can be considered to be part of the boundary of a surface in the rest frame of the magnetic field, and the area of that surface is changing. The EMF turns out to be ## \mathcal{E}=vBL ##. This topic was addressed in great detail in a recent Insights article by @vanhees71 , https://www.physicsforums.com/insights/homopolar-generator-analytical-example/ , but if you are a first or second year physics student, you probably don't need to understand the full detail.
 
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  • #3
Number 3 is incorrect.It is a type of motional emf
 
  • #4
It's also good to think about such problems not only in terms of Faraday's law but also in terms of electromagnetic interactions. In case 3 you have a wire, which you can see as a container of the gas of conduction electrons. Now moving through the magnetc field ##\vec{B}## leads to the force ##\vec{F}_1=q \vec{v} \times \vec{B}/c## an each electron with charge ##q(=-e)##. That implies that the electrons move towards one end of the wire (and are lacking at the other end). Thus an electric field is built up, leading to a force ##\vec{F}_2=q \vec{E}##. The stationary state is reached, as soon as the total force on the electrons is 0. Putting the two expressions for the forces together leads to the result given in #2.
 
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  • #5
Thank you everyone! I figured out where my misunderstanding was sprouting from.
As I stated before, in the equation Φ=B⋅A, A is the surface area of the conductor.
My misunderstanding was of the bounds of each term in Φ=B⋅A

When looking at a specific area in the magnetic field, before the wire has moved into that area the value a A for that specific space is 0 because there is no conductor there. As the wire moves into the space then there begins to be an increasing and then decreasing value of A for that specific space thus resulting in a change in flux for that specific space, and an induced emf.
 

Related to Flux in a Uniform Magnetic Field

What is flux in a uniform magnetic field?

Flux in a uniform magnetic field is a measure of the number of magnetic field lines passing through a given area. It is represented by the symbol Φ, and its unit is weber (Wb).

How is flux in a uniform magnetic field calculated?

Flux in a uniform magnetic field is calculated by multiplying the strength of the magnetic field (B) by the area (A) perpendicular to the field lines. This can be represented by the equation Φ = BA.

What is the direction of flux in a uniform magnetic field?

The direction of flux in a uniform magnetic field is perpendicular to the plane of the area. This means that if the area is parallel to the magnetic field, the flux is zero.

How does the orientation of the area affect the flux in a uniform magnetic field?

The orientation of the area has a significant impact on the flux in a uniform magnetic field. When the area is perpendicular to the magnetic field, the flux is at its maximum value. On the other hand, when the area is parallel to the field, the flux is zero.

What are some real-life applications of flux in a uniform magnetic field?

Flux in a uniform magnetic field is used in various technologies such as transformers, electric motors, generators, and MRI machines. It is also essential in understanding the behavior of charged particles in a magnetic field.

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