00:01
Theorem to show that d tends to a, a tends to c, c tends to b, b tends to c and c tends to a.
00:17
The conditions for the divergenceless solenoid fields, dell .f is zero everywhere.
00:34
Second is integral of f .d .d .a is independent of surface.
00:40
For any given boundary line.
00:47
F .d .a is zero for any closed surface and fourth condition is f equals to del cross a if f is the curl of some vector.
01:08
It is provided that f is the curl of some vector so f is equal to del cross a the equation a has del dot f equals to 0 in this statement so we can say that d tends to a now del dot del cross a is again 0 this is always true because the divergence of curl is always 0 this is the fundamental property of the vector analysis therefore d tends to a the equation a is del dot f is 0 expression for the course divergence theorem integral of del dot f into dv equals integral of f .d .a.
01:59
Here f is a vector substituting del dot f equals to 0 to show a tends to c.
02:08
Putting the value 0, we can have f .da also equals to 0.
02:15
It tends to say that a tends to c.
02:19
Now the equation c says that integral of f .da equals to zero for any closed surface.
02:27
Considering the two arbitrary surfaces 1 and 2 of the spherical body, the aerial vector for the surface 1 is outward and the aerial vector for the surface 2 is inward.
02:46
The expression for the surface integral for a vector f can be written as f.
02:51
D .a 1 plus f .da2 equals to integration of f .d .a.
03:00
For the closed surface.
03:01
Substituting f .d .a equals to 0.
03:05
So we have f1 .da equals to f2.
03:12
For the second surface, da is invert.
03:17
Therefore the negative sign is used...