Hello friends welcome to engineering Funda family in this video I'll explain stocks theorem with great clarity before I start with my explanation let me tell you the outlines of this video in this video I'll explain Basics statement proof physical significance and applications of stocks theorem so let us begin this session with first agenda that is basics of stocks theorem one should know talks theorem is based on C of function in my earlier videos of this video lecture series of electromagnetics theory I have explained Cur of function talks theorem that is based on Cur of function and if You observe stocks theorem statement then that gives relationship in between line integration and surface integration so stocks theorem that is based on C of function if you have function f then D cross F that is Cur of function so Cur of function surface integration is equals to function's line integration means stocks theorem gives you idea about relationship in between surface integration and line integration in this video I'll derive this statement as well the stocks theorem that is based on Call of function and based on Call of function one can identify rotation of body at different positions let me take few examples that will gives you more clarity let us consider here we have turbine you can observe and this turbine is placed under flow of water so at bottom of this turbine flow of water is there in this direction because of this flow of water this turbine that is getting rotated in anticlockwise Direction means C of function that is positive over here so based on C of function one can identify rotational mement of body here body is turbine if I have turbine like this and as if water flow is happening in this direction then this turbine that is getting roled in this direction that is clockwise Direction means here col of function that is negative so here turbine motion that explains col of function so as if you have filled instead of water if you have filled which is revolving body then that motion of Revolution that could be identified by Cur of function so stocks theorem that we use it to identify rotational motion of body now I'll explain you proof of stocks theorem the stocks theorem is based on col of function if you have function f that is given as per FX into y direction plus FY into J Direction plus FZ into K Direction then C of function is D cross F and that will be i j k d by DX d by Dy d by d z and FX FY and FZ so by having a solution of this Matrix one can identify col of function and col of function that could be also calculated by this limit where Delta s tends to zero here Delta s is small area of given function so here area is going towards zero where line integration of function divide by Delta s that is there with this limit now if you want stocks theorem then all you need to do is you need to cross multiply this Delta s over this side if you do that then here over this side we have limit Delta s TS to 0 col of function into Delta s and over this side we have limit Delta s TS to 0er and functions line integration is there see this functions line integration that has nothing to do with area so this portion will be line integration of function only But If You observe this side then over this side we have definition of integration definition of integration is what limit Delta s TS to Z anything Delta s that means that anything that we are integrating with respect to area so this term that is call of function surface integration and this term that is function line integration and this is what statement of stocks theorem so stocks theorem explains what it explains relationship in between surface integration and line integration see this relationship that is very essential the reason is as in when you do mathematical calculation at the time simplification can be done using Talk theorem in future coming videos I'll be solving few problems by which you can understand why stocks theorem is very essential why this relation of surface integration with line integration is very essential that you will get to know based on some problems now I'll explain you physical significance of stocks theorem stocks theorem is based on col of function and based on col of function one can identify rotational and irrotational motion of given body so based on stocks theorem one can identify rotational and irrotational movement under field let me take few examples here we have one body you can observe and this body is placed under field so you can observe field is happening like this on this body so here direction of field that is equal on both of this surface top surface as well as bottom surface because of which this body that will not be having any rotational movement so this field is IR rotational field that one can say means C of the function that will be zero C of the function is zero means what here body is not having any rotational movement right so if you want to identify rotational movement of body then you'll have to identify col of the function and that could be identified using stocks theorem let me take few more case studies If You observe here we have field which is happening in this direction at top of the body and at the bottom of the body field is happening in this direction so because of this field there will be rotational movement and that will happen in this direction that will happen in clockwise direction if you identify C of the function then that c of the function that will be negative it explains rotational movement due to field and that is happening in clockwise Direction means C of the function that will be negative here let me consider one more case study in which at top side field is happening in this direction and at bottom side field is happening in this direction because of which body will be having rotational movement in anticlockwise direction or one can say counterclockwise Direction so here rotational field is there because of field there is anticlockwise movement of this body means C of the function that will be posi So based on stocks theorem we can identify rotational movement of body right now let me discuss about applications of stocks theorem the stocks theorem that we can use it in fluid mechanics in fluid mechanics with fluid if we want to identify rotational movement of atoms then one can apply stocks theorem so in flow of fluid how Ms are there with body that can identify using stock theorem it is also used in flow of field there can be a different types of field under which body may be there that body could be mass that body could be charge right so based on different fields there can be different types of torque calculation that could be done under gravitational field electric field or magnetic field this stock theorem that is also used in aerodynamics as well as we can use it in electromagnetics in this video lecture series of electromagnetics theory I'll explain many problems based on stock theorum in future coming videos that will resolve your queries further I hope now you are having fair enough idea about what is stocks theorem what is the physical meaning of it based on this in future we will be solving few problems as well thank you so much for watching this video