Magneto Hydrostatic Equation & Magneto Hydrostatic Pressure

1. MAGNETO HYDROSTATIC EQUATION,
MAGNETO HYDROSTATIC PRESSURE

2. Plasma was first identified in a Crookes tube,
and so described by Sir William Crookes in
1879 (he called it "radiant matter").
The term "plasma" was coined by Irving Langmuir in
1928, perhaps because the glowing discharge molds
itself to the shape of the Crooks tube
(Greek πλάσμα – a thing molded or formed).
The nature of the Crookes tube "cathode ray” matter
was subsequently identified by British physicist Sir
J.J. Thomson in 1897

3.  A plasma is a quasineutral gas of charge and
neutral particles which exhibits collective
behavior”
 It is one of the four fundamental states of matter,
the others being solid, liquid, and gas. A plasma
has properties unlike those of the other states.
 Motion of charges generate current & hence
magnetic fields.
 These fields affect the motion of other charged
particles for away

4. Plasma behave sometimes like fluids and sometimes
like a collection of individual particles. The motion of
charged particles in presence of electric and magnetic
field can be describe in two ways: one is particle
description of plasma dealt in previous article and
other is in plasma is considered as a two interaction
charged fluids though under limited condition.
Magneto hydrodynamics applied to the latter case.
if the charge d fluid moves in a magnetic field then
electric current are induced in the fluid as a result of
its motion. Induced current give rise to their own
magnetic field and thus modify the applied field. As
these charges move around they can generate local
concentrations of positive and negative charge which
gives rise to electric n field thus situation become
more complex compared to that the particle
description. We couple Maxwell field equation with
the equation of hydrodynamic.

5. It is the law of continuity which describe the conservation of matter
and is written as
(∂ ρ/∂t)+ ∇.(ρv) = 0 ……..(1)
Or (∂ ρ/∂t)+ ρ div v+v.grad ρ
This is one of hydrodynamic equation the other is that of force
with relates to gain of momentum in a fluid element to the force
which act upon it. This is
ρdv/dt=- ∇P+ ρg+F
The viscous force F and gravitational force ρg can be neglected so
that
ρdv/dt=- ∇P ………(2)
Where the time derivative of velocity on left hand side of eqn (2)
is
d-/dt= ∂ -/∂t+v.grad
Which gives total time rate of change of a quantity moving
instantaneously with velocity v.

6. When we consider the electromagnetic field we have to
consider the magnetic stress (J*B) where J is current
density.
We shall see later on that (J*B) arises in part from a
magnetic pressure.
Then eqn (2) can be written as
Ρdv/dt=- ∇P+(J*B) ………..(3)
Representing magneto hydrodynamic eqn
In the domain of magnetob hydrodynamic, it is
customary to neglect the displacement current in
Ampere’s law (∇.J=0),
So that field eqn ,describing their behavior in the
fluid are
(∇*E)+( ∂ B/∂t)=0
(∇*B)= μ0J
The other two divergence eqns have been omitted.

7. The force on the unit volume of the plasma may be written as
F= J*B -▽P …….(1)
Now writing
▽*B=μJ ……..(2)
And B*∇*b = ∇(1/2)B2-(B*.∇)B ……..(3)
So that putting equation (2) into (3) we get
B*μ0J = ∇(1/2)B2-(B*.∇)B
J*B= -∇ (B2/2μ0)+(B.∇)B/ μ0
Where the term B2/2μ0 is the magnetic energy per unit volume
in fluid and it plays the role of a magnetic pressure Pm
Pm= B2/2μ0
Therefore the term J*B in equation (1) can be interpreted as
arising in part from a magnetic pressure

8. MAGNETO HYDROSTATIC PRESSURE

9. Made By:
Anita Malviya