Given a current loop, the quantity IA is called the magnetic dipole moment (M) where I is the electric current flowing in the loop and A is the area enclosed by the loop. This is called the far-field approximation. Classically, magnetic flux density generated by the loop depends only on the area and not on its shape: M = IA.
On the other hand, if a magnetic dipole experiences an infinitesimal near local turning force (torque) in a non-uniform or time-varying magnetic field then the magnetic dipole moment is defined as the ratio of the torque (T) over the magnetic flux density (B): M = T/B. It is then logical that the far-field approximation is the integral of the near-field equation IA = ∫T/B. As a classical experimental constant, B can be taken outside the integral: ∫∂T = IAB. Torque is defined as the vector cross product of the radius vector r and a local infinitesimal force F: ∂T = r × F. Since r× F = - F× r, two possible distinct orientations exist such that quantized torque is made equivalent to quantized spin. Although torque is a vector, the scalar inner dot product of torque is equivalent to a square of energy.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Are not all dipoles connected by an unversal energy field,where near and far does not apply
Dipoles (electric or magnetic) exist due to broken symmetries. I am thinking that quadrupoles should be able to restore symmetry. Once restored then they are all connected into a universal energy field.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Dipoles (electric or magnetic) exist due to broken symmetries. I am thinking that quadrupoles should be able to restore symmetry. Once restored then they are all connected into a universal energy field.
Symmetry needs to be restored,or else there be chaos?
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself?
Re: dipole near and far -
05-10-2007, 03:17 PM
Linear Mode
