Are magnetic fields 'conservative'

In summary: So it's not really a "negate" operation, it's more like taking the gradient of a vector.I believe the idea isn't that the scalar potential isn't simpler vs direct manipulation of fields, but rather that multivalued scalar potential isn't simpler than vector potential, plus the latter is generally true with no restrictions. So it's not really a "negate" operation, it's more like taking the gradient of a vector.In summary, the scalar potential is a useful tool for permanent magnets, but is not simpler than manipulating a direct field.
  • #1
pardesi
339
0
surely [tex]\vec{\nabla} \times \vec{B} \neq 0[/tex] in general
but the work done by magnetic field on any charge is 0 hence is independent of the path taken
So can we call such a field conservative
 
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  • #2
Be careful in using "surely" and "general". Curl B is not zero in the presence of current.
The usual textbook definition of a "conservative field" is that
[tex]\oint{\bf B}\cdot{\bf dr}=0[/tex], which is not true if the path circles any current.
 
  • #3
want to follow up a question. i read in wiki and it says that non-conservative force is due to negligence of certain degrees of freedom. Is this a well accepted concept? if yes, then what sort of degrees are neglected in case of magnetic force so that it becomes non-conserving? thankyou :smile:

http://en.wikipedia.org/wiki/Conservative_force
 
  • #4
luben said:
want to follow up a question. i read in wiki and it says that non-conservative force is due to negligence of certain degrees of freedom. Is this a well accepted concept? if yes, then what sort of degrees are neglected in case of magnetic force so that it becomes non-conserving? thankyou :smile:

http://en.wikipedia.org/wiki/Conservative_force

I'm thinking wiki is just wrong.
 
  • #5
pardesi said:
surely [tex]\vec{\nabla} \times \vec{B} \neq 0[/tex] in general
but the work done by magnetic field on any charge is 0 hence is independent of the path taken
So can we call such a field conservative

Indeed, if you have a static magnetic field, you can have a scalar potential (search for magnetic scalar potential on Google). This potential is multivalued, and undefined at points with current. Thus actually a magnetic field is kinda conservative --- if the field is static and the region you're interested in has no currents. However, it's not a very useful point of view, and doesn't actually simplify the algebra --- multivalued functions aren't very friendly.
 
  • #6
genneth said:
However, it's not a very useful point of view, and doesn't actually simplify the algebra --- multivalued functions aren't very friendly.
That is Griffith's, somewhat naive, point of view, but the scalar potential does actually simplify the algebra, and can be quite useful, especially for permanent magnets.
The multi-valued part is no real problem. Are you also going to exclude logarithms and roots?
 
  • #7
pam said:
That is Griffith's, somewhat naive, point of view, but the scalar potential does actually simplify the algebra, and can be quite useful, especially for permanent magnets.
The multi-valued part is no real problem. Are you also going to exclude logarithms and roots?

I believe the idea isn't that the scalar potential isn't simpler vs direct manipulation of fields, but rather that multivalued scalar potential isn't simpler than vector potential, plus the latter is generally true with no restrictions.
 

FAQ: Are magnetic fields 'conservative'

1. Are magnetic fields considered to be 'conservative'?

Yes, magnetic fields are considered to be conservative. This means that the work done by a magnetic field on a moving charged particle depends only on the initial and final positions of the particle, and not on the path taken in between.

2. What does it mean for a magnetic field to be conservative?

When a magnetic field is conservative, it means that the energy associated with the field is conserved and can be converted from one form to another without any loss. This is similar to the concept of conservation of energy in physics.

3. How do you determine if a magnetic field is conservative or not?

A magnetic field is conservative if the line integral of the field along any closed path is zero. This means that the work done by the field on a particle moving along a closed loop is zero. If the line integral is not zero, then the magnetic field is non-conservative.

4. Are there any real-life examples of conservative magnetic fields?

Yes, there are several real-life examples of conservative magnetic fields, such as the Earth's magnetic field. The Earth's magnetic field is responsible for protecting us from harmful solar radiation and also plays a crucial role in the navigation of migratory animals like birds and bees.

5. What are the implications of a magnetic field being non-conservative?

A non-conservative magnetic field means that the energy associated with the field is not conserved and can be lost or converted to other forms. This can lead to inefficiency in energy conversion processes and can also have implications for the behavior of charged particles in the field.

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