Equation for magnetic moment, E-field and B-field

[pangsiukwong]

Hi!

When a charge/current moves in a closed loop, a magnetic moment is generated.
Is there any formula for connecting the magnetic moment to E-field and B-field?

Patrick

 

[Meir Achuz]

A magnetic moment m (a vector) produces a magnetic field given by
B=[3(m.r)r/r^5-m/r^3] plus a delta function if r-->0.
The r in the numerators are vectors and . means the dot product.
There is no E field produced.

 

[m2003]

,

Yes, there is a formula for connecting the magnetic moment to the electric and magnetic fields. The equation is given by:

m = qA

Where:
m = magnetic moment
q = charge
A = area of the loop

This equation shows that the magnetic moment is directly proportional to the charge and the area of the loop. Additionally, the magnetic moment is also affected by the strength of the magnetic field (B-field) and the orientation of the loop with respect to the B-field.

To incorporate the E-field, we can use the Lorentz force equation:

F = q(E + v x B)

Where:
F = force on the charge
q = charge
E = electric field
v = velocity of the charge
B = magnetic field

This equation shows that the E-field can also affect the motion of the charge, and therefore, indirectly affect the magnetic moment. So, the magnetic moment can be influenced by both the E-field and B-field.

I hope this helps answer your question. Let me know if you have any further inquiries.