BASIC LAW OF MANGNETOSTATICS Neha

2. I respect and thank our
physics teacher for giving an opportunity to do the
project work on Basic Law of Magnetostatics in
differential form and providing me all support and
guidance which made me complete the project on
time. I am extremely greatful to him for providing
such a nice support and guidance though he had
busy schedule managing the time .

3. Basic Law of Magnetostatics in Differential Form :
.B = 0 and × B =µ0J :-
There Are the following two fundamental laws of
magnetostatics :
(1) Div B = 0 or .B = 0
(2)Curl B = µ0 J or × B =µ0J
Law(2)- Curl B = µ0J or × B = µ0J :- The
Curl of the static magnetic field B produced near a
current carrying conductor is equal to the product if
permeability of the medium and current density. Thus the
magnetic field is a rotational (or Curl) field .
In differential form, Curl B = µ0 J or × B =µ0J (in air
or vacuum)

4. Proof :- If a stationary current (i.e., current not
changing with time) flows in a conductor, a magnetic field
is produced around it . According to Ampere’s circuital
law,
“the line integral of magnetic field vector B along a closed
curve in this magnetic field is equal to µ0 times the
algebraic sum of currents enclosed within that curve. Here
µ0 (= 4Π × 10-7 N/A2 ) is the permeability if free space.
Thus
B . dl = µ0 I ---------- 1st
Here the symbol expresses the line integral
along the closed curve .
C
C

5. The sign if integral depends on the direction of magnetic field. If
the direction of magnetic field is along the path, the line integral
is positive and if the direction of magnetic field is opposite to the
path, the line integral is negative .
For a stationary current, the total current enclosed within a
closed curve is equal to the flux of current density linked with the
area enclosed by that curve . Fig shows a volume distribution of
current in which the current density is J at a point (x , y , z) .
Consider a closed curve C around this point which encloses a
surface S . The current enclosed within the closed curve is

6. I = J . da
so, By Ampere’s law (from eqn. 1st ),
B . dl = µ0 J. da --------------2nd
But by Stokes's theorem , B. dl = Curl B. da
From eqn. 2nd , Curl B. da = µ0 J. da
or (Curl B - µ0 J ) . da = 0 or Curl B - µ0J = 0
or Curl B = µ0 J or × B = µ0 J.
C
C