What is the relationship between magnetic flux and coil wire?

In summary, the magnetic flux is defined as the product of the magnetic field and the area it is acting upon, and is measured in Vs/m^2. The total flux inside a coil is equivalent to the flux outside. The magnetic field in a circular magnetic circuit must be the same everywhere, similar to the current in a circular circuit. For calculations, it is best to integrate over the area of the loop of wire. In the case of a straight wire with no current, there is no flux to calculate. However, if there is a changing magnetic field, an electric field is induced in the wire. The equation \Phi \equiv \int \mathbf{B} \cdot d \math
  • #1
Entanglement
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13
Magnetic Flux= BA is A the surrounding area affected by the flux or the area of the coil itself that is affected by the flux
 
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  • #2
B is measured in Vs/m^2 i.e. flux per area.
A can be any arbitary area.
btw. The total flux inside a coil is identical in magnitude to the flux outside.
Look at the images at http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
The field goes in a circle. Just like the current in a circular circuit has to be the same everywhere, the magnetic flux in a circular magnetic circuit has to be the same.
 
  • #3
I mean if a I straight wire with no current is placed in a magnetic field, how can I calculate the Flux affecting the wire using flux=BA
 
  • #4
ElmorshedyDr said:
Magnetic Flux= BA is A the surrounding area affected by the flux or the area of the coil itself that is affected by the flux

In any calculation with the flux being [tex] \Phi \equiv \int \mathbf{B} \cdot d \mathbf{a} [/tex] it's always best to integrate over the area of the loop of wire.

ElmorshedyDr said:
I mean if a I straight wire with no current is placed in a magnetic field, how can I calculate the Flux affecting the wire using flux=BA

If you have a straight wire, there is no flux to calculate. If there is no current, or if the wire is not moving in the magnetic field, then the magnetic field has no effect on the electrons in the wire because of the Lorentz force law: [tex] \mathbf{F}_{mag} = Q(\mathbf{v} \times \mathbf{B}) [/tex]
 
  • #5
phy_infinite said:
In any calculation with the flux being [tex] \Phi \equiv \int \mathbf{B} \cdot d \mathbf{a} [/tex] it's always best to integrate over the area of the loop of wire.

If you have a straight wire, there is no flux to calculate. If there is no current, or if the wire is not moving in the magnetic field, then the magnetic field has no effect on the electrons in the wire because of the Lorentz force law: [tex] \mathbf{F}_{mag} = Q(\mathbf{v} \times \mathbf{B}) [/tex]
Thanks a lot but I can't understand these equations
 
  • #6
phy_infinite said:
In any calculation with the flux being [tex] \Phi \equiv \int \mathbf{B} \cdot d \mathbf{a} [/tex] it's always best to integrate over the area of the loop of wire.



If you have a straight wire, there is no flux to calculate. If there is no current, or if the wire is not moving in the magnetic field, then the magnetic field has no effect on the electrons in the wire because of the Lorentz force law: [tex] \mathbf{F}_{mag} = Q(\mathbf{v} \times \mathbf{B}) [/tex]

If you have a round, single-turn coil with a smll gap in it somewhere, and a time-varying B field is present in-line with the coil's normal vector, then there is also no motion nor current, yet there is an emf developed across the gap. So this argument is questionable.

Not that I know the answer. If I have a rectangular path in air but with the wire forming one of the four sides, there is similarly emf developed around that path with the same time-varying B field. The question is, what portion of the emf is along the wire?
 
  • #7
rude man said:
If you have a round, single-turn coil with a smll gap in it somewhere, and a time-varying B field is present in-line with the coil's normal vector, then there is also no motion nor current, yet there is an emf developed across the gap. So this argument is questionable.
Not that I know the answer. If I have a rectangular path in air but with the wire forming one of the four sides, there is similarly emf developed around that path with the same time-varying B field. The question is, what portion of the emf is along the wire?
What I want to know is If I have a straight wire placed perpendicularly to a magnetic field, how can I calculate the flux affecting the wire " the wire is still, there is no motion"
 
  • #8
rude man said:
If you have a round, single-turn coil with a smll gap in it somewhere, and a time-varying B field is present in-line with the coil's normal vector, then there is also no motion nor current, yet there is an emf developed across the gap. So this argument is questionable.

Not that I know the answer. If I have a rectangular path in air but with the wire forming one of the four sides, there is similarly emf developed around that path with the same time-varying B field. The question is, what portion of the emf is along the wire?

Oh I was only referring to a constant magnetic field which has no effect. Of course a changing magnetic field induces an electric field. Any current induced in an open circuit by a changing magnetic field would be almost instantly gone as the charge piling up at one end would create an opposing electric field.
 
  • #9
ElmorshedyDr said:
Thanks a lot but I can't understand these equations
The equation [tex]\Phi \equiv \int \mathbf{B} \cdot d \mathbf{a}[/tex] is simply a more specific definition than the one you gave; [itex] \Phi = B \cdot A [/itex] which is really just a special case. The equation [tex]\mathbf{F}_{mag} = Q(\mathbf{v} \times \mathbf{B})[/tex] is saying that the magnetic force on a charge Q is proportional to the strength of the magnetic field and the velocity of the charge. If a wire isn't moving or there is no current, then there is no magnetic force.
ElmorshedyDr said:
What I want to know is If I have a straight wire placed perpendicularly to a magnetic field, how can I calculate the flux affecting the wire " the wire is still, there is no motion"

If you have a loop of wire lying in a plane perpendicular to the magnetic field, then the flux is the magnetic field times the area created by the loop. But only a changing flux will induce an emf in the loop. Like I said in #8, any current in an open circuit wouldn't last long at all as it would almost instantly go away. Now, in general the flux of the magnetic field is BA. If you were to connect both ends of the straight wire within the magnetic field, the area of the loop is what you would use to calculate the flux through the loop. If the wire is not in a loop but open straight, I don't see the point in calculating the flux. I honestly haven't come across this problem, but I assume it's because you aren't going to get any current out of it, at least not for long.

None the less, when calculating the changing flux, the area created by the circuit is used to calculate the EMF which in turn can tell us the current. If we have a loop with a small gap, and small enough for current to jump the gap, I would use the area created by the wire and line between the two ends of the wire, treating the air gap as a resistor. If the wire were slightly bent into a U shape, it may or may not be valid to use the area created by the wire and the shortest line between the ends of the wire.
 
  • #10
phy_infinite said:
If the wire is not in a loop but open straight, I don't see the point in calculating the flux. I honestly haven't come across this problem, but I assume it's because you aren't going to get any current out of it, at least not for long.
.
I mention that point, because I couldn't understand how does magnetic flux changes when moving the wire where it cuts the field lines as the wire covers a certain area, it seams non logical to calculate the flux using the area covered by wire !
 
  • #11
ElmorshedyDr said:
I mention that point, because I couldn't understand how does magnetic flux changes when moving the wire where it cuts the field lines as the wire covers a certain area, it seams non logical to calculate the flux using the area covered by wire !

The magnetic flux may not change when moving any wire. By moving the wire, you are setting the charges in motion with respect to the magnetic field, so even if the magnetic field is not changing, the magnetic force is acting on the charges.
 
  • #12
phy_infinite said:
The magnetic flux may not change when moving any wire. By moving the wire, you are setting the charges in motion with respect to the magnetic field, so even if the magnetic field is not changing, the magnetic force is acting on the charges.
Isn't the change calculated from : Delta area x flux density / delta time ?
 
  • #13
ElmorshedyDr said:
Isn't the change calculated from : Delta area x flux density / delta time ?

If the magnetic field is constant, then as you move the wire, the flux is constant and does not change.
 
  • #14
phy_infinite said:
If the magnetic field is constant, then as you move the wire, the flux is constant and does not change.
Then when do I use the equation Blv
 
  • #15
ElmorshedyDr said:
Then when do I use the equation Blv

Whenever there is a B, an l and a v. In your case there is no v. So the emf = 0 irrespective of the time behavior of B.
 
  • #16
ElmorshedyDr said:
Isn't the change calculated from : Delta area x flux density / delta time ?

Yes. but delta area = 0.
 
  • #17
rude man said:
Whenever there is a B, an l and a v. In your case there is no v. So the emf = 0 irrespective of the time behavior of B.
I said earlier the wire is moving there is a v
 
  • #18
If the wire is moving, then the wire sweeps out an area. Therefore the area is changing, then you do have a changing flux.
 
  • #19
Then you use the Blv law.

The Blv law applies even in situations where there is moving media and Maxwell's equation del x E = - dB/dt does not apply.

In your case the area is formed by the motion of the wire: delta area = lv per second, so dA/dt = B dA/dt = Blv.
 
  • #20
phy_infinite said:
Also if the magnetic field doesn't change, a changing area also changes the flux.
I can't understand how changing area changes flux since the geometrical shape of wire is constant so the flux should be constant!
 
  • #21
phy_infinite said:
If the magnetic field is constant, then as you move the wire, the flux is constant and does not change.

Here, I should have said the flux changes, since the area changes.
 
  • #22
ElmorshedyDr said:
I can't understand how changing area changes flux since the geometrical shape of wire is constant so the flux should be constant!

Flux is area times B. If area changes, flux changes and there is an emf generated.

Area changes as vl. Think of the wire sweeping the area behind it as it moves in the perpendicular B field. dA/dt = lv.
 
  • #23
ElmorshedyDr said:
I can't understand how changing area changes flux since the geometrical shape of wire is constant so the flux should be constant!

It's more intuitive and accurate really to think about the Lorentz force law. For a wire of length l moving through a constant magnetic field at some velocity, it can be found using the Lorentz force law that EMF = Blv.
 
  • #24
for a physical picture imagine a simple dc electric motor, you have stationary magnets and a rotor which has wires through it that form coils, these wires are constantly moving and " cutting" through the field of those magnets and current is being produced.
 
  • #25
ElmorshedyDr said:
I can't understand how changing area changes flux since the geometrical shape of wire is constant so the flux should be constant!

To see this more rigorously, imagine you're pulling on a wire of length l to the right side of the computer screen and the wire itself is pointing up on the computer screen in a magnetic field that is pointing into the screen. Then the emf is [tex] \varepsilon = \oint \mathbf{f} \cdot d \mathbf{l} [/tex] Where [itex] \mathbf{f} [/itex] is the force per unit charge. The magnetic force will add a vertical component to the electrons in the wire so they will be moving at an angle towards the top right corner of the screen. The electrons would then be moving upward with speed u and to the right with speed v. Now, the magnetic force will also have a component to the left side of the screen. This force to the left would be equal to QuB. You would then have to pull with force per unit charge uB to the right. The total distance traveled by a charge is [itex] \frac{l}{cos \theta} [/itex] Therefore the work done per unit charge would be [tex] \int \mathbf{f}_{pull} \cdot d \mathbf{l} = (uB) (\frac{l}{cos \theta}) sin \theta = vBl = \varepsilon [/tex]

Fortunately, this gives a result equivalent to the flux rule for motional emf.
 
Last edited:

What is magnetic flux?

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

How is magnetic flux calculated?

Magnetic flux is calculated by multiplying the magnetic field strength (B) by the area (A) perpendicular to the field. The formula for magnetic flux is Φ = B x A.

What is coil wire?

Coil wire refers to a length of thin, insulated wire that has been wound into a coil shape. It is commonly used in the construction of electromagnets and inductors.

How does coil wire affect magnetic flux?

The presence of a coil wire can increase or decrease the magnetic flux depending on the direction of the current flowing through it. When current flows in the same direction as the magnetic field, the flux increases. When current flows in the opposite direction, the flux decreases.

What are some practical applications of magnetic flux and coil wire?

Magnetic flux and coil wire are used in a variety of applications, including generators, motors, transformers, and MRI machines. They also play a crucial role in electrical power transmission and distribution systems.

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