Are magnetic fields conservative field?

Click For Summary
SUMMARY

Magnetic fields are not classified as conservative fields due to their dependence on velocity, which prevents the definition of a scalar potential function. This distinction is crucial in understanding electromagnetic fields, where energy is conserved but the magnetic force does not meet the criteria of a conservative force field. The discussion highlights the technical nuances introduced by professors in academic settings, emphasizing the importance of grasping these concepts in the study of electromagnetism.

PREREQUISITES
  • Understanding of electromagnetic fields and their properties
  • Familiarity with the concept of conservative force fields
  • Basic knowledge of vector calculus and gradients
  • Awareness of the relationship between force, velocity, and potential energy
NEXT STEPS
  • Research the mathematical definitions of conservative and non-conservative forces
  • Study the implications of energy conservation in electromagnetic fields
  • Learn about the role of velocity in magnetic forces
  • Explore the concept of potential energy in the context of electric and magnetic fields
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators explaining the nuances of magnetic fields, and anyone interested in the foundational principles of force fields in physics.

fluidistic
Gold Member
Messages
3,932
Reaction score
283
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!
 
Physics news on Phys.org
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.
 
Last edited by a moderator:
I see, thank you very much.
 

Similar threads

Undergrad Can nested solenoids trap particles?
  • · Replies 12 ·
Replies
12
Views
1K
Undergrad Charge movement relative to magnetic field frame dependence/invariance
  • · Replies 5 ·
Replies
5
Views
2K
High School Force Exerted on a Conductor by a Homogeneous Magnetic Field
  • · Replies 1 ·
Replies
1
Views
2K
High School Experiment issues (electromagnetism)
  • · Replies 42 ·
2
Replies
42
Views
4K
High School How is a magnetic field formed in a space surrounded by one pole?
  • · Replies 3 ·
Replies
3
Views
2K
High School Magnetic field and generator power output
  • · Replies 5 ·
Replies
5
Views
3K
High School A question about induced current in LC circuits
  • · Replies 4 ·
Replies
4
Views
2K
High School Measuring electric field vs magnetic field
  • · Replies 8 ·
Replies
8
Views
3K
High School Consequences of a 1 Tesla magnetic field coming into the proximity of Earth?
  • · Replies 11 ·
Replies
11
Views
2K
High School Magnetic field coil ferrous material for loudspeaker
  • · Replies 31 ·
2
Replies
31
Views
5K