A Magnetic Misconception on Divergence 0/Closed Field Lines?

In summary, "A Magnetic Misconception on Divergence 0/Closed Field Lines?" explores the common misunderstanding that magnetic field lines that are closed or have zero divergence imply the absence of magnetic monopoles. The article clarifies that while magnetic field lines are indeed closed and exhibit zero divergence in classical electromagnetism, this does not rule out the theoretical existence of magnetic monopoles. The discussion emphasizes the importance of understanding the implications of these concepts in both classical and modern physics.
  • #1
walkeraj
17
4
Question: Can we ultimately atttribute no work or net zero work done by a magnetic force to the closed magnetic field lines that results in Divergence zero of a magnetic field? That is, is it a misconception to say that closed magnetic field lines imply magnetic force will always result in no net work?

(I meant misconception on my part not theory.)

Edit: Why misconception? Now switch to electric field. The field lines between two opposite electric test charges are also closed and resemble that of a bar magnet, though electric in nature. Does it hold? Is it enough to say that since the field lines are closed between the two test charges that no net work can ever be done?
 
Last edited:
Physics news on Phys.org
  • #2
Work done by a magnetic force on what ? Electric charge ?
 
  • #3
Electric charge is all I can see (thinking back to Griffith's book).
 
  • #4
Consider the electric field of an idealized electric dipole. It has only closed field lines, but it can do work on a charge.
 
  • Like
Likes Vanadium 50

FAQ: A Magnetic Misconception on Divergence 0/Closed Field Lines?

What is the main misconception about magnetic fields and divergence?

The main misconception is that magnetic fields can have a non-zero divergence, meaning that magnetic monopoles exist. However, according to Gauss's law for magnetism, the divergence of a magnetic field is always zero, indicating that magnetic monopoles do not exist and magnetic field lines are always closed loops.

Why do magnetic field lines form closed loops?

Magnetic field lines form closed loops because magnetic monopoles do not exist. This is a direct consequence of Gauss's law for magnetism, which states that the net magnetic flux through any closed surface is zero. Therefore, magnetic field lines must return to their origin, forming closed loops.

How does Gauss's law for magnetism relate to the concept of divergence?

Gauss's law for magnetism states that the divergence of the magnetic field (B) is zero, mathematically expressed as ∇·B = 0. This implies that there are no "sources" or "sinks" of magnetic field lines, reinforcing the idea that magnetic field lines are continuous and form closed loops.

Can magnetic monopoles exist according to current scientific understanding?

According to current scientific understanding and Maxwell's equations, magnetic monopoles do not exist. The absence of magnetic monopoles is a fundamental aspect of classical electromagnetism, which is reflected in the fact that the divergence of the magnetic field is zero.

What are the implications of divergence being zero for magnetic fields in practical applications?

The fact that the divergence of magnetic fields is zero has several practical implications. It means that magnetic field lines must form closed loops, which is crucial for the design of magnetic circuits and devices such as transformers, inductors, and magnetic confinement systems in fusion reactors. It also ensures that magnetic fields can be effectively used for applications like MRI machines and magnetic storage devices.

Similar threads

B Seeing both B field lines and E field lines at the same time
Replies
22
Views
1K
I Field Strength of Permanent Magnets -- Inverse square or inverse cube?
Replies
9
Views
502
I Magnetic field when the area of the plates of a capacitor increases
Replies
7
Views
354
B Why does a magnet attract metal objects?
Replies
2
Views
843
B Why does my LC circuit not oscillate its energy between Electric & Magnetic fields?
5
Replies
152
Views
3K
B Magnetic force driving a small iron ball
Replies
4
Views
2K
B Permanent magnets and energy question
Replies
16
Views
2K
I Divergence of v x B = Divergence of E in the v=0 frame?
Replies
7
Views
2K
B Understanding the electric field
Replies
16
Views
833
B Curious about the uniform electric field between metal plates
Replies
8
Views
797

Hot Threads

Recent Insights

Back
Top