- #1
Jay21
- 3
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Hello all,
I have a question regarding Maxwell's Equations and Faraday's unipolar induction equation.
If we study the case of a cylindrical magnet with a radius of r which is rotating about its axis
with angular velocity w. The electrons within the magnet collide with the moving atoms, causing
a net drift velocity, v = w x r. The electrons experience a force:
-e*(v x B) towards the center
This results in the negative charge being centralized in the magnet and a positive
charge on the outer surface, thus creating an equilibrium electrostatics field with
Lorentz force:
F = -eE - e*(v x B) = 0
This leads to the unipolar induction equation of
E = - v x B
My question is that while studying plasma physics I came across a very similar equation such that
H = v x D
How would one derive this analogous equation of the unipolar induction equation?
I read somewhere that you could derive this equation by using a thin, charged rotating ring,
but I am unsure as to how to accomplish this.
Thanks so much.
Jay
Citations I have investigated trying to derive this analgous equation:
Unipolar Induction via a Rotating, Conducting, Magnetized Cylinder by Kirk T. McDonald
for in a comoving inertia frame
H* = H - ((v/c) x D)
Basic Plasma Physics Principles by Gordon Emslie for
E' = gamma*(E + (v/c) x B)
B' = gamma*(B - (v/c) x E)
The Unipolar Induction by P. Hrasko for
B = (u_0*gamma)*H + (1/c^2)(v x E)
I have a question regarding Maxwell's Equations and Faraday's unipolar induction equation.
If we study the case of a cylindrical magnet with a radius of r which is rotating about its axis
with angular velocity w. The electrons within the magnet collide with the moving atoms, causing
a net drift velocity, v = w x r. The electrons experience a force:
-e*(v x B) towards the center
This results in the negative charge being centralized in the magnet and a positive
charge on the outer surface, thus creating an equilibrium electrostatics field with
Lorentz force:
F = -eE - e*(v x B) = 0
This leads to the unipolar induction equation of
E = - v x B
My question is that while studying plasma physics I came across a very similar equation such that
H = v x D
How would one derive this analogous equation of the unipolar induction equation?
I read somewhere that you could derive this equation by using a thin, charged rotating ring,
but I am unsure as to how to accomplish this.
Thanks so much.
Jay
Citations I have investigated trying to derive this analgous equation:
Unipolar Induction via a Rotating, Conducting, Magnetized Cylinder by Kirk T. McDonald
for in a comoving inertia frame
H* = H - ((v/c) x D)
Basic Plasma Physics Principles by Gordon Emslie for
E' = gamma*(E + (v/c) x B)
B' = gamma*(B - (v/c) x E)
The Unipolar Induction by P. Hrasko for
B = (u_0*gamma)*H + (1/c^2)(v x E)