Are magnetic fields conservative field?

In summary, the conversation discusses a professor's statement that they are not conservative, which surprises the speaker. The topic of magnetic fields is also introduced and the concept of conservation in electromagnetic fields is mentioned. The speaker expresses confusion about the distinction between magnetic fields and conservative force fields."
  • #1
fluidistic
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The title says it all. I've heard my professor saying that they are not conservative. I'm very surprised by this. If it is true then I'll think about all the implications it generates.

By the way today was the class where we were introduced magnetic fields for the first time.
Thanks!
 
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  • #2
It seems to me that your professor is getting a little over-technical here, but perhaps he has a reason for making this distinction which will become apparent later in the course.

Energy is definitely conserved in electromagnetic fields (see http://farside.ph.utexas.edu/teaching/em/lectures/node89.html). But technically a magnetic field is not a force field (since the magnetic force also depends on the velocity), so it cannot be a conservative force field. Because the magnetic force depends on velocity you cannot define the gradient of the force, and therefore you cannot set it equal to some scalar function (the potential) as you can with a conservative force field.
 
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  • #3
I see, thank you very much.
 

FAQ: Are magnetic fields conservative field?

What is a conservative field?

A conservative field is a type of vector field in which the line integral between any two points is independent of the path taken between those points. This means that the work done by the field is only dependent on the initial and final positions, and not on the path taken.

How do you determine if a magnetic field is conservative?

To determine if a magnetic field is conservative, you can use the property that the line integral of a conservative field is independent of the path taken. This means that if the line integral between any two points is the same, regardless of the path taken, then the magnetic field is conservative.

What are the implications of a magnetic field being conservative?

If a magnetic field is conservative, it means that the work done by the field is only dependent on the initial and final positions, and not on the path taken. This makes it easier to calculate the work done by the magnetic field and also simplifies the equations used to describe the field.

What are some examples of conservative magnetic fields?

Some examples of conservative magnetic fields include the magnetic fields produced by a permanent magnet, a current-carrying wire, and a solenoid. These fields have a well-defined direction and can be described using vector equations.

Are all magnetic fields conservative?

No, not all magnetic fields are conservative. In order for a magnetic field to be conservative, the curl of the magnetic field must be equal to zero. This means that the field lines must form closed loops and there must be no sources or sinks of magnetic flux. Magnetic fields produced by changing electric fields, such as in electromagnetic waves, are not conservative.

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