Vector potential and constant magnetic flux density

AI Thread Summary
The discussion focuses on verifying that the vector potential A = 1/2(-yB0, xB0, 0) yields a constant magnetic flux density B0 in the z direction. The correct approach involves using the relation B = ∇ × A, with clarification that the symbol ∇ should be used. Participants suggest writing out the components of the curl of A in Cartesian coordinates to facilitate the proof. The conversation emphasizes the need for a mathematical method to confirm the relationship between vector potential and magnetic flux density. This analytical verification is essential for understanding the properties of magnetic fields in the specified configuration.
skyboarder2
Messages
15
Reaction score
0
Hi,

I would like to verify analytically that a vector potential of the form A=1/2(-yB0,xB0,0) produces a constant magnetic flux density of magnitude B0 in the z direction.
(I guess I'd have to use the relation B=\forall\wedgeA...)
 
Physics news on Phys.org
That is correct (assuming you meant to write the symbol \nabla). Do you have a question?
 
Nope, I just look for a method to prove it mathematically
 
Write out the components of \vec{\nabla} \times \vec{A} in Cartesian coordinates.
 

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
View full post »
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
View full post »

Similar threads

I How to use geometrical symmetries -- general advice? (Vector potential)
Replies
2
Views
1K
I Motional EMF in Faraday disc, co-rotating magnet axial mean flux
Replies
5
Views
155
How does the saturation flux density affect magnetic field strength?
Replies
1
Views
1K
Magnetic Flux outside of a long solenoid
Replies
2
Views
2K
I Hall effect -- is it always applicable?
Replies
7
Views
2K
Magnetic field lines and magnetic flux density
Replies
35
Views
4K
I Resulting magnetic field due to the passage of an AC current
Replies
27
Views
2K
A Relationship between magnetic potential and current density in Maxwell
Replies
2
Views
2K
Magnetic saturation and ferrite magnets
Replies
2
Views
4K
I How Do Dielectrics Influence Electric Flux Density in Electromagnetic Theory?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top